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The Graph Crossing Number and its Variants: A Survey

https://doi.org/10.37236/2713
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The crossing number ofK3,n in a surface
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The book crossing number of a graph
inferredcites →https://doi.org/10.1002/(sici)1097-0118(199607)22:3<239::aid-jgt4>3.0.co;2-nopenalex-snapshot
The crossing number ofC5 �Cn
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Crossing numbers of graph embedding pairs on closed surfaces
inferredcites →https://doi.org/10.1002/1097-0118(200103)36:3<>1.0.co;2-sopenalex-snapshot
inferredcites →https://doi.org/10.1002/9781118032718.scardopenalex-snapshot
Wiley‐Interscience Series in Discrete Mathematics and Optimization
inferredcites →https://doi.org/10.1002/jgt.20109openalex-snapshot
Two maps with large representativity on one surface
inferredcites →https://doi.org/10.1002/jgt.20249openalex-snapshot
The crossing number of K 11 is 100
inferredcites →https://doi.org/10.1002/jgt.22027openalex-snapshot
On the Pseudolinear Crossing Number
inferredcites →https://doi.org/10.1002/jgt.3190010105openalex-snapshot
A note of welcome
inferredcites →https://doi.org/10.1002/jgt.3190020302openalex-snapshot
On stable crossing numbers
inferredcites →https://doi.org/10.1002/jgt.3190040203openalex-snapshot
On the crossing numbers of products of cycles and graphs of order four
inferredcites →https://doi.org/10.1002/jgt.3190070302openalex-snapshot
Maximum versus minimum invariants for graphs
inferredcites →https://doi.org/10.1002/jgt.3190100102openalex-snapshot
The crossing number of K1,3,n and K2,3,n
inferredcites →https://doi.org/10.1002/jgt.3190120306openalex-snapshot
Rectilinear drawings of graphs
inferredcites →https://doi.org/10.1002/jgt.3190150109openalex-snapshot
Bounds for the crossing number of the N ‐cube
inferredcites →https://doi.org/10.1002/jgt.3190160502openalex-snapshot
New results on rectilinear crossing numbers and plane embeddings
inferredcites →https://doi.org/10.1002/jgt.3190170308openalex-snapshot
Bounds for rectilinear crossing numbers
inferredcites →https://doi.org/10.1002/jgt.3190170602openalex-snapshot
Cyclic‐order graphs and Zarankiewicz's crossing‐number conjecture
inferredcites →https://doi.org/10.1002/jgt.3190170605openalex-snapshot
The projective plane crossing number of C3 × Cn
inferredcites →https://doi.org/10.1002/jgt.3190190406openalex-snapshot
A new proof of the 6 color theorem
inferredcites →https://doi.org/10.1002/mana.19861250122openalex-snapshot
Zur Struktur 1‐planarer Graphen
inferredcites →https://doi.org/10.1002/rsa.10053openalex-snapshot
Crossing numbers of random graphs
inferredcites →https://doi.org/10.1002/sapm1977562159openalex-snapshot
Maximal Rectilinear Crossing of Cycles
inferredcites →https://doi.org/10.1006/aima.1996.0069openalex-snapshot
The Crossing Number of a Graph on a Compact 2-Manifold
inferredcites →https://doi.org/10.1006/jctb.2000.1978openalex-snapshot
Which Crossing Number Is It Anyway?
inferredcites →https://doi.org/10.1006/jvlc.1995.1010openalex-snapshot
Layout Adjustment and the Mental Map
inferredcites →https://doi.org/10.1006/jvlc.2002.0232openalex-snapshot
Metrics for Graph Drawing Aesthetics
inferredcites →https://doi.org/10.1007/0-387-31909-3openalex-snapshot
Evolutionary Computation for Modeling and Optimization
inferredcites →https://doi.org/10.1007/11809678_52openalex-snapshot
Bimodal Crossing Minimization
inferredcites →https://doi.org/10.1007/11809678_53openalex-snapshot
Fixed Linear Crossing Minimization by Reduction to the Maximum Cut Problem
inferredcites →https://doi.org/10.1007/3-540-33700-8_28openalex-snapshot
Crossing Number of Toroidal Graphs
inferredcites →https://doi.org/10.1007/3-540-37623-2_18openalex-snapshot
Crossing Number of Abstract Topological Graphs
inferredcites →https://doi.org/10.1007/3-540-44541-2_23openalex-snapshot
Graph Layout for Displaying Data Structures
inferredcites →https://doi.org/10.1007/3-540-44634-6_33openalex-snapshot
An Approach for Mixed Upward Planarization
inferredcites →https://doi.org/10.1007/3-540-45848-4_22openalex-snapshot
A Short Note on the History of Graph Drawing
inferredcites →https://doi.org/10.1007/3-540-46648-7_13openalex-snapshot
Drawing Graphs in the Hyperbolic Plane
inferredcites →https://doi.org/10.1007/3-540-46648-7_18openalex-snapshot
The Constrained Crossing Minimization Problem
inferredcites →https://doi.org/10.1007/3-540-46648-7_23openalex-snapshot
On 3-Layer Crossings and Pseudo Arrangements
inferredcites →https://doi.org/10.1007/3-540-48518-x_4openalex-snapshot
Circular Drawings of Biconnected Graphs
inferredcites →https://doi.org/10.1007/3-540-48523-6_32openalex-snapshot
Compact Routing Tables for Graphs of Bounded Genus (Extended Abstract)
inferredcites →https://doi.org/10.1007/3-540-55210-3_199openalex-snapshot
The complexity of colouring circle graphs
inferredcites →https://doi.org/10.1007/3-540-59071-4_53openalex-snapshot
Book embeddings and crossing numbers
inferredcites →https://doi.org/10.1007/3-540-62495-3_42openalex-snapshot
Straight-line drawing algorithms for hierarchical graphs and clustered graphs
inferredcites →https://doi.org/10.1007/978-0-8176-4580-9openalex-snapshot
A Beginner’s Guide to Graph Theory
inferredcites →https://doi.org/10.1007/978-1-4614-0110-0_2openalex-snapshot
The Rectilinear Crossing Number of K n : Closing in (or Are We?)
inferredcites →https://doi.org/10.1007/978-1-4614-0110-0_30openalex-snapshot
A Better Bound for the Pair-Crossing Number
inferredcites →https://doi.org/10.1007/978-3-0346-0425-3_1openalex-snapshot
Algebraic and Probabilistic Methods in Discrete Mathematics
inferredcites →https://doi.org/10.1007/978-3-319-00200-2_12openalex-snapshot
Expected Crossing Numbers
inferredcites →https://doi.org/10.1007/978-3-319-03841-4_10openalex-snapshot
Recognizing Outer 1-Planar Graphs in Linear Time
inferredcites →https://doi.org/10.1007/978-3-319-03841-4_17openalex-snapshot
Block Additivity of ℤ2-Embeddings
inferredcites →https://doi.org/10.1007/978-3-319-03841-4_29openalex-snapshot
Metro-Line Crossing Minimization: Hardness, Approximations, and Tractable Cases
inferredcites →https://doi.org/10.1007/978-3-319-03841-4_30openalex-snapshot
Fixed Parameter Tractability of Crossing Minimization of Almost-Trees
inferredcites →https://doi.org/10.1007/978-3-540-24595-7_1openalex-snapshot
Confluent Drawings: Visualizing Non-planar Diagrams in a Planar Way
inferredcites →https://doi.org/10.1007/978-3-540-30559-0_28openalex-snapshot
Crossing Reduction in Circular Layouts
inferredcites →https://doi.org/10.1007/978-3-540-30577-4_43openalex-snapshot
Outerplanar Crossing Numbers of 3-Row Meshes, Halin Graphs and Complete p-Partite Graphs
inferredcites →https://doi.org/10.1007/978-3-540-30577-4_8openalex-snapshot
Progress on Crossing Number Problems
inferredcites →https://doi.org/10.1007/978-3-540-32439-3_4openalex-snapshot
Biplanar Crossing Numbers I: A Survey of Results and Problems
inferredcites →https://doi.org/10.1007/978-3-540-70904-6_27openalex-snapshot
Minimizing Intra-edge Crossings in Wiring Diagrams and Public Transportation Maps
inferredcites →https://doi.org/10.1007/978-3-540-73556-4_32openalex-snapshot
A New Exact Algorithm for the Two-Sided Crossing Minimization Problem
inferredcites →https://doi.org/10.1007/978-3-540-77120-3_18openalex-snapshot
Algorithms for the Hypergraph and the Minor Crossing Number Problems
inferredcites →https://doi.org/10.1007/978-3-540-77537-9_6openalex-snapshot
Crossing Numbers and Parameterized Complexity
inferredcites →https://doi.org/10.1007/978-3-642-00219-9_29openalex-snapshot
Minimal Obstructions for 1-Immersions and Hardness of 1-Planarity Testing
inferredcites →https://doi.org/10.1007/978-3-642-00219-9_48openalex-snapshot
Spine Crossing Minimization in Upward Topological Book Embeddings
inferredcites →https://doi.org/10.1007/978-3-642-02882-3_8openalex-snapshot
Coordinate Assignment for Cyclic Level Graphs
inferredcites →https://doi.org/10.1007/978-3-642-03367-4_19openalex-snapshot
Drawing Graphs with Right Angle Crossings
inferredcites →https://doi.org/10.1007/978-3-642-03456-5_21openalex-snapshot
The Crossing Number of Graphs: Theory and Computation
inferredcites →https://doi.org/10.1007/978-3-642-11805-0_32openalex-snapshot
Complexity of Some Geometric and Topological Problems
inferredcites →https://doi.org/10.1007/978-3-642-18381-2_6openalex-snapshot
The Straight-Line RAC Drawing Problem Is NP-Hard
inferredcites →https://doi.org/10.1007/978-3-642-18469-7_18openalex-snapshot
Lombardi Drawings of Graphs
inferredcites →https://doi.org/10.1007/978-3-642-18469-7_22openalex-snapshot
Optimal k-Level Planarization and Crossing Minimization
inferredcites →https://doi.org/10.1007/978-3-642-25011-8_9openalex-snapshot
How Not to Characterize Planar-Emulable Graphs
inferredcites →https://doi.org/10.1007/978-3-642-25878-7_27openalex-snapshot
Monotone Crossing Number
inferredcites →https://doi.org/10.1007/978-3-642-30347-0_7openalex-snapshot
Mad at Edge Crossings? Break the Edges!
inferredcites →https://doi.org/10.1007/978-3-642-31223-6_11openalex-snapshot
Improved Layout for Data Flow Diagrams with Port Constraints
inferredcites →https://doi.org/10.1007/978-3-642-32241-9_29openalex-snapshot
Fáry’s Theorem for 1-Planar Graphs
inferredcites →https://doi.org/10.1007/978-3-642-33090-2_59openalex-snapshot
A Fast and Simple Subexponential Fixed Parameter Algorithm for One-Sided Crossing Minimization
inferredcites →https://doi.org/10.1007/978-3-642-36763-2_22openalex-snapshot
Upward Planarity Testing via SAT
inferredcites →https://doi.org/10.1007/978-3-642-38768-5_41openalex-snapshot
A Linear Edge Kernel for Two-Layer Crossing Minimization
inferredcites →https://doi.org/10.1007/978-3-642-40313-2_36openalex-snapshot
Ordering Metro Lines by Block Crossings
inferredcites →https://doi.org/10.1007/978-3-642-45043-3_22openalex-snapshot
The Same Upper Bound for Both: The 2-Page and the Rectilinear Crossing Numbers of the n-Cube
inferredcites →https://doi.org/10.1007/978-3-642-46908-4_75openalex-snapshot
On 2-Embeddable Graphs
inferredcites →https://doi.org/10.1007/978-3-642-58409-1_11openalex-snapshot
The Constrained Crossing Minimization Problem A First Approach
inferredcites →https://doi.org/10.1007/978-3-642-58412-1openalex-snapshot
Complexity and Approximation
inferredcites →https://doi.org/10.1007/978-3-662-45803-7_19openalex-snapshot
A Crossing Lemma for the Pair-Crossing Number
inferredcites →https://doi.org/10.1007/bf01187020openalex-snapshot
Edge crossings in drawings of bipartite graphs
inferredcites →https://doi.org/10.1007/bf01215922openalex-snapshot
Graphs drawn with few crossings per edge
inferredcites →https://doi.org/10.1007/bf01504336openalex-snapshot
�ber die Maximalzahl der Doppelpunkte bei ebenen Polygonen von gerader Seitenzahl
inferredcites →https://doi.org/10.1007/bf01744433openalex-snapshot
New lower bound techniques for VLSI
inferredcites →https://doi.org/10.1007/bf01897149openalex-snapshot
Recent results in topological graph theory
inferredcites →https://doi.org/10.1007/bf02020451openalex-snapshot
On a problem of P. Erdős
inferredcites →https://doi.org/10.1007/bf02086611openalex-snapshot
Drawings of Graphs on Surfaces with Few Crossings
inferredcites →https://doi.org/10.1007/bf02307651openalex-snapshot
Lehrbuch der Kombinatorik
inferredcites →https://doi.org/10.1007/bf02401740openalex-snapshot
Über kombinatorische Topologie
inferredcites →https://doi.org/10.1007/bf02418540openalex-snapshot
Die Geometrie der Wirklichkeit
inferredcites →https://doi.org/10.1007/bf02522826openalex-snapshot
Three-dimensional graph drawing
inferredcites →https://doi.org/10.1007/bf02574034openalex-snapshot
Intersections of curve systems and the crossing number ofC 5 ×C 5
inferredcites →https://doi.org/10.1007/bf02574701openalex-snapshot
Some provably hard crossing number problems
inferredcites →https://doi.org/10.1007/bf02941309openalex-snapshot
Bemerkungen zu einem Sechsfarbenproblem von G. Ringel
inferredcites →https://doi.org/10.1007/bf02941434openalex-snapshot
Ein 7-farbensatz 1-einbettbarer graphen auf der projektiven ebene
inferredcites →https://doi.org/10.1007/bf02951847openalex-snapshot
Die natürliche Geometrie
inferredcites →https://doi.org/10.1007/bf02992822openalex-snapshot
Thickness and coarseness of graphs
inferredcites →https://doi.org/10.1007/bf02996313openalex-snapshot
Ein Sechsfarbenproblem auf der Kugel
inferredcites →https://doi.org/10.1007/bfb0035832openalex-snapshot
On the k-colouring of circle-graphs
inferredcites →https://doi.org/10.1007/bfb0059432openalex-snapshot
Latest results on crossing numbers
inferredcites →https://doi.org/10.1007/bfb0066436openalex-snapshot
Some recent results in topological graph theory
inferredcites →https://doi.org/10.1007/bfb0067363openalex-snapshot
Crossing numbers of graphs
inferredcites →https://doi.org/10.1007/pl00009365openalex-snapshot
Extremal Problems for Geometric Hypergraphs
inferredcites →https://doi.org/10.1007/s00224-010-9275-6openalex-snapshot
Area, Curve Complexity, and Crossing Resolution of Non-Planar Graph Drawings
inferredcites →https://doi.org/10.1007/s00283-009-9120-4openalex-snapshot
The Early History of the Brick Factory Problem
inferredcites →https://doi.org/10.1007/s00373-005-0616-1openalex-snapshot
Topological Graphs with No Large Grids
inferredcites →https://doi.org/10.1007/s00453-004-1093-2openalex-snapshot
An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization
inferredcites →https://doi.org/10.1007/s00453-007-0010-xopenalex-snapshot
Algorithms for Graphs Embeddable with Few Crossings per Edge
inferredcites →https://doi.org/10.1007/s00453-009-9343-yopenalex-snapshot
Crossing Numbers of Graphs with Rotation Systems
inferredcites →https://doi.org/10.1007/s00454-006-1264-9openalex-snapshot
Improving the Crossing Lemma by Finding More Crossings in Sparse Graphs
inferredcites →https://doi.org/10.1007/s00454-007-1325-8openalex-snapshot
New Lower Bounds for the Number of (≤ k)-Edges and the Rectilinear Crossing Number of Kn
inferredcites →https://doi.org/10.1007/s00454-007-9024-zopenalex-snapshot
Note on the Pair-crossing Number and the Odd-crossing Number
inferredcites →https://doi.org/10.1007/s00454-008-9058-xopenalex-snapshot
Odd Crossing Number and Crossing Number Are Not the Same
inferredcites →https://doi.org/10.1007/s00454-009-9141-yopenalex-snapshot
Degenerate Crossing Numbers
inferredcites →https://doi.org/10.1007/s00454-009-9196-9openalex-snapshot
Planar Graphs Have 1-string Representations
inferredcites →https://doi.org/10.1007/s00454-010-9245-4openalex-snapshot
General Lower Bounds for the Minor Crossing Number of Graphs
inferredcites →https://doi.org/10.1007/s00454-012-9430-8openalex-snapshot
Planar Crossing Numbers of Graphs of Bounded Genus
inferredcites →https://doi.org/10.1007/s00454-012-9440-6openalex-snapshot
Hardness of Approximation for Crossing Number
inferredcites →https://doi.org/10.1007/s00454-013-9493-1openalex-snapshot
On the Degenerate Crossing Number
inferredcites →https://doi.org/10.1007/s00454-013-9514-0openalex-snapshot
The 2-Page Crossing Number of $$K_{n}$$ K n
inferredcites →https://doi.org/10.1007/s00454-014-9635-0openalex-snapshot
Shellable Drawings and the Cylindrical Crossing Number of $$K_{n}$$ K n
inferredcites →https://doi.org/10.1007/s00454-014-9644-zopenalex-snapshot
Crossing Numbers and Combinatorial Characterization of Monotone Drawings of $$K_n$$ K n
inferredcites →https://doi.org/10.1007/s004540010042openalex-snapshot
Mutation Polynomials and Oriented Matroids
inferredcites →https://doi.org/10.1007/s10107-006-0039-7openalex-snapshot
Reduction of symmetric semidefinite programs using the regular $$\ast$$ -representation
inferredcites →https://doi.org/10.1007/s10732-006-4294-9openalex-snapshot
An analysis of some linear graph layout heuristics
inferredcites →https://doi.org/10.1007/s11424-008-9115-9openalex-snapshot
The projective plane crossing numbers of circular graphs*
inferredcites →https://doi.org/10.1007/s12293-013-0115-5openalex-snapshot
$$K$$ -page crossing number minimization problem: An evaluation of heuristics and its solution using GESAKP
inferredcites →https://doi.org/10.1016/0010-4485(85)90007-7openalex-snapshot
Computer-generated multi-row schematics
inferredcites →https://doi.org/10.1016/0012-365x(73)90127-1openalex-snapshot
The crossing number of the complement of a circuit
inferredcites →https://doi.org/10.1016/0022-0000(89)90032-9openalex-snapshot
Embedding planar graphs in four pages
inferredcites →https://doi.org/10.1016/0095-8956(71)90045-1openalex-snapshot
An upper bound for the rectilinear crossing number of the complete graph
inferredcites →https://doi.org/10.1016/0095-8956(72)90042-1openalex-snapshot
A lower bound for crossing numbers of graphs with applications to Kn, Kp,q, and Q(d)
inferredcites →https://doi.org/10.1016/0095-8956(78)90014-xopenalex-snapshot
The crossing number of C3 × Cn
inferredcites →https://doi.org/10.1016/0095-8956(79)90021-2openalex-snapshot
The book thickness of a graph
inferredcites →https://doi.org/10.1016/0095-8956(91)90050-topenalex-snapshot
String graphs requiring exponential representations
inferredcites →https://doi.org/10.1016/0095-8956(91)90090-7openalex-snapshot
String graphs. I. The number of critical nonstring graphs is infinite
inferredcites →https://doi.org/10.1016/j.comgeo.2008.05.005openalex-snapshot
Edges and switches, tunnels and bridges
inferredcites →https://doi.org/10.1016/j.comgeo.2011.06.002openalex-snapshot
Bold graph drawings
inferredcites →https://doi.org/10.1016/j.dam.2005.12.011openalex-snapshot
On k-planar crossing numbers
inferredcites →https://doi.org/10.1016/j.dam.2007.05.009openalex-snapshot
Approximating the fixed linear crossing number
inferredcites →https://doi.org/10.1016/j.dam.2012.05.028openalex-snapshot
Generalized k -ary tanglegrams on level graphs: A satisfiability-based approach and its evaluation
inferredcites →https://doi.org/10.1016/j.dam.2012.11.002openalex-snapshot
(2)-pancyclic graphs
inferredcites →https://doi.org/10.1016/j.dam.2013.11.001openalex-snapshot
Book drawings of complete bipartite graphs
inferredcites →https://doi.org/10.1016/j.dam.2015.10.009openalex-snapshot
A lower bound on the crossing number of uniform hypergraphs
inferredcites →https://doi.org/10.1016/j.disc.2005.09.010openalex-snapshot
The crossing number of K4,n on the real projective plane
inferredcites →https://doi.org/10.1016/j.disc.2005.11.056openalex-snapshot
The structure of 1-planar graphs
inferredcites →https://doi.org/10.1016/j.disc.2006.12.002openalex-snapshot
The crossing number of K1,4,n
inferredcites →https://doi.org/10.1016/j.disc.2007.11.023openalex-snapshot
The crossing number of K1,m,n
inferredcites →https://doi.org/10.1016/j.disc.2007.12.088openalex-snapshot
On the complexity of crossings in permutations
inferredcites →https://doi.org/10.1016/j.disc.2008.07.040openalex-snapshot
Coloring graphs with crossings
inferredcites →https://doi.org/10.1016/j.disc.2008.09.029openalex-snapshot
The toroidal crossing number of K4,n
inferredcites →https://doi.org/10.1016/j.ejc.2009.03.002openalex-snapshot
Removing even crossings on surfaces
inferredcites →https://doi.org/10.1016/j.endm.2008.01.045openalex-snapshot
The maximum number of halving lines and the rectilinear crossing number of for
inferredcites →https://doi.org/10.1016/j.endm.2008.06.053openalex-snapshot
Unexpected behaviour of crossing sequences
inferredcites →https://doi.org/10.1016/j.endm.2013.10.064openalex-snapshot
More on the crossing number of : Monotone drawings
inferredcites →https://doi.org/10.1016/j.ipl.2013.01.013openalex-snapshot
Density of straight-line 1-planar graph drawings
inferredcites →https://doi.org/10.1016/j.jcss.2009.10.014openalex-snapshot
Comparing trees via crossing minimization
inferredcites →https://doi.org/10.1016/j.jcta.2007.11.004openalex-snapshot
An extended lower bound on the number of (⩽k) -edges to generalized configurations of points and the pseudolinear crossing number of Kn
inferredcites →https://doi.org/10.1016/j.jctb.2003.05.001openalex-snapshot
Arrangements, circular arrangements and the crossing number of C7×C
inferredcites →https://doi.org/10.1016/j.jctb.2003.09.002openalex-snapshot
Crossing number, pair-crossing number, and expansion
inferredcites →https://doi.org/10.1016/j.jctb.2005.09.009openalex-snapshot
Crossing number is hard for cubic graphs
inferredcites →https://doi.org/10.1016/j.jctb.2005.10.004openalex-snapshot
The nonorientable genus of complete tripartite graphs
inferredcites →https://doi.org/10.1016/j.jctb.2006.08.001openalex-snapshot
Removing even crossings
inferredcites →https://doi.org/10.1016/j.jctb.2012.11.001openalex-snapshot
Zarankiewiczʼs Conjecture is finite for each fixed m
inferredcites →https://doi.org/10.1016/j.jctb.2019.05.009openalex-snapshot
Toroidal grid minors and stretch in embedded graphs
inferredcites →https://doi.org/10.1016/j.jvlc.2011.12.002openalex-snapshot
Improving multiple aesthetics produces better graph drawings
inferredcites →https://doi.org/10.1016/j.jvlc.2013.11.005openalex-snapshot
Drawing layered graphs with port constraints
inferredcites →https://doi.org/10.1016/j.micpro.2012.06.010openalex-snapshot
A formal study on topology and floorplan characteristics of mesh and torus-based optical networks-on-chip
inferredcites →https://doi.org/10.1016/j.tcs.2008.02.032openalex-snapshot
On the obfuscation complexity of planar graphs
inferredcites →https://doi.org/10.1016/j.tcs.2010.10.038openalex-snapshot
On the red/blue spanning tree problem
inferredcites →https://doi.org/10.1016/s0012-365x(00)00193-xopenalex-snapshot
On the nonembeddability and crossing numbers of some toroidal graphs on the Klein bottle
inferredcites →https://doi.org/10.1016/s0012-365x(01)00078-4openalex-snapshot
Special numbers of crossings for complete graphs
inferredcites →https://doi.org/10.1016/s0012-365x(03)00317-0openalex-snapshot
A successful concept for measuring non-planarity of graphs: the crossing number
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Removing edge-node intersections in drawings of graphs
inferredcites →https://doi.org/10.1016/s0021-9800(68)80013-4openalex-snapshot
On a problem of P. Erdös
inferredcites →https://doi.org/10.1016/s0021-9800(68)80063-8openalex-snapshot
The toroidal crossing number of the complete graph
inferredcites →https://doi.org/10.1016/s0021-9800(69)80084-0openalex-snapshot
The toroidal crossing number of K
inferredcites →https://doi.org/10.1016/s0021-9800(70)80007-2openalex-snapshot
Toward a theory of crossing numbers
inferredcites →https://doi.org/10.1016/s0021-9800(70)80087-4openalex-snapshot
The crossing number of K
inferredcites →https://doi.org/10.1016/s0095-8956(03)00026-1openalex-snapshot
Optimal meshes of curves in the Klein bottle
inferredcites →https://doi.org/10.1016/s0095-8956(03)00037-6openalex-snapshot
Crossing-number critical graphs have bounded path-width
inferredcites →https://doi.org/10.1016/s0304-0208(08)73484-4openalex-snapshot
Crossing-Free Subgraphs
inferredcites →https://doi.org/10.1016/s0304-3975(02)00031-2openalex-snapshot
Towards area requirements for drawing hierarchically planar graphs
inferredcites →https://doi.org/10.1016/s0304-3975(99)00285-6openalex-snapshot
A new lower bound for the bipartite crossing number with applications
inferredcites →https://doi.org/10.1017/9781009701259.032openalex-snapshot
On the Pair-Crossing Number
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On Crossing Numbers, and some Unsolved Problems
inferredcites →https://doi.org/10.1017/s0013091500025645openalex-snapshot
On the Number of Crossings in a Complete Graph
inferredcites →https://doi.org/10.1017/s030500410006028xopenalex-snapshot
Determining the thickness of graphs is NP-hard
inferredcites →https://doi.org/10.1017/s0963548313000400openalex-snapshot
Near-Optimal Separators in String Graphs
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Who shall survive?: A new approach to the problem of human interrelations.
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Algebra: an Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges
inferredcites →https://doi.org/10.1038/100302a0openalex-snapshot
Amusements in Mathematics
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Permutation procedure for minimising the number of crossings in a network
inferredcites →https://doi.org/10.1073/pnas.52.3.688openalex-snapshot
THE MINIMUM NUMBER OF INTERSECTIONS IN COMPLETE GRAPHS
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The Rectilinear Crossing Number of a Complete Graph and Sylvester's “Four Point Problem” of Geometric Probability
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What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4969841openalex-extracted
On 1-Planar Graphs with Bounded Cop-Number
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Using block designs in crossing number bounds
inferred← citeshttps://doi.org/10.1002/jgt.22027openalex-snapshot
On the Pseudolinear Crossing Number
inferred← citeshttps://doi.org/10.1002/jgt.22763openalex-snapshot
Bounding the tripartite‐circle crossing number of complete tripartite graphs
inferred← citeshttps://doi.org/10.1002/jgt.23097openalex-snapshot
Edge-Minimum Saturated k-Planar Drawings
inferred← citeshttps://doi.org/10.1007/978-1-4939-2864-4_658openalex-snapshot
Planarisation and Crossing Minimisation
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A Generalized Force-Directed Layout for Multiplex Sociograms
inferred← citeshttps://doi.org/10.1007/978-3-030-35802-0_5openalex-snapshot
Bundled Crossings Revisited
inferred← citeshttps://doi.org/10.1007/978-3-030-35802-0_6openalex-snapshot
Crossing Numbers of Beyond-Planar Graphs
inferred← citeshttps://doi.org/10.1007/978-3-030-35802-0_7openalex-snapshot
On the 2-Colored Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-030-68766-3_28openalex-snapshot
Crossings Between Non-homotopic Edges
inferred← citeshttps://doi.org/10.1007/978-3-030-68766-3_31openalex-snapshot
Simple Topological Drawings of k-Planar Graphs
inferred← citeshttps://doi.org/10.1007/978-3-030-68766-3_37openalex-snapshot
Plane Spanning Trees in Edge-Colored Simple Drawings of $$K_{n}$$
inferred← citeshttps://doi.org/10.1007/978-3-030-94106-2_2openalex-snapshot
Planar Graphs
inferred← citeshttps://doi.org/10.1007/978-3-030-96731-4_31openalex-snapshot
Approximating the Bundled Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-031-06678-8_18openalex-snapshot
The Slotted Online One-Sided Crossing Minimization Problem on 2-Regular Graphs
inferred← citeshttps://doi.org/10.1007/978-3-031-22203-0_2openalex-snapshot
Compatible Spanning Trees in Simple Drawings of $$K_n$$
inferred← citeshttps://doi.org/10.1007/978-3-031-49272-3_6openalex-snapshot
String Graphs with Precise Number of Intersections
inferred← citeshttps://doi.org/10.1007/978-3-319-27261-0_6openalex-snapshot
The Degenerate Crossing Number and Higher-Genus Embeddings
inferred← citeshttps://doi.org/10.1007/978-3-319-27261-0_8openalex-snapshot
Genus, Treewidth, and Local Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-319-31940-7_13openalex-snapshot
Turán’s Brick Factory Problem: The Status of the Conjectures of Zarankiewicz and Hill
inferred← citeshttps://doi.org/10.1007/978-3-319-42634-1_37openalex-snapshot
Approximating the Maximum Rectilinear Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-319-50106-2_31openalex-snapshot
The Bundled Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-319-50106-2_32openalex-snapshot
Approximating the Rectilinear Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-319-68705-6_5openalex-snapshot
On the Relationship Between k-Planar and k-Quasi-Planar Graphs
inferred← citeshttps://doi.org/10.1007/978-3-319-73915-1_42openalex-snapshot
Beyond Outerplanarity
inferred← citeshttps://doi.org/10.1007/978-3-319-78825-8_6openalex-snapshot
On the Maximum Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-319-97686-0_14openalex-snapshot
An Annotated Glossary of Graph Theory Parameters, with Conjectures
inferred← citeshttps://doi.org/10.1007/978-3-642-27848-8_658-1openalex-snapshot
Planarisation and Crossing Minimisation
inferred← citeshttps://doi.org/10.1007/978-3-662-45803-7_16openalex-snapshot
Fan-Planar Graphs: Combinatorial Properties and Complexity Results
inferred← citeshttps://doi.org/10.1007/978-3-662-45803-7_19openalex-snapshot
A Crossing Lemma for the Pair-Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-662-45803-7_3openalex-snapshot
Drawing Partially Embedded and Simultaneously Planar Graphs
inferred← citeshttps://doi.org/10.1007/978-3-662-48971-0_51openalex-snapshot
On Hardness of the Joint Crossing Number
inferred← citeshttps://doi.org/10.1007/978-3-662-49529-2_34openalex-snapshot
Bundled Crossings in Embedded Graphs
inferred← citeshttps://doi.org/10.1007/978-981-15-6533-5_2openalex-snapshot
Quantitative Restrictions on Crossing Patterns
inferred← citeshttps://doi.org/10.1007/s00373-019-02076-5openalex-snapshot
The Bipartite-Cylindrical Crossing Number of the Complete Bipartite Graph
inferred← citeshttps://doi.org/10.1007/s00373-020-02204-6openalex-snapshot
There Are No Cubic Graphs on 26 Vertices with Crossing Number 10 or 11
inferred← citeshttps://doi.org/10.1007/s00373-021-02303-yopenalex-snapshot
The Conjecture on the Crossing Number of $$K_{1,m,n}$$ is true if Zarankiewicz’s Conjecture Holds
inferred← citeshttps://doi.org/10.1007/s00373-022-02538-3openalex-snapshot
The Crossing Number of Twisted Graphs
inferred← citeshttps://doi.org/10.1007/s00373-023-02711-2openalex-snapshot
Maximum Rectilinear Crossing Number of Uniform Hypergraphs
inferred← citeshttps://doi.org/10.1007/s00373-025-02990-xopenalex-snapshot
On the d-independence number in 1-planar graphs
inferred← citeshttps://doi.org/10.1007/s00454-014-9635-0openalex-snapshot
Shellable Drawings and the Cylindrical Crossing Number of $$K_{n}$$ K n
inferred← citeshttps://doi.org/10.1007/s00454-014-9644-zopenalex-snapshot
Crossing Numbers and Combinatorial Characterization of Monotone Drawings of $$K_n$$ K n
inferred← citeshttps://doi.org/10.1007/s00454-017-9898-3openalex-snapshot
Shortest Path Embeddings of Graphs on Surfaces
inferred← citeshttps://doi.org/10.1007/s00454-025-00738-1openalex-snapshot
Associahedra Minimize F-Vectors of Secondary Polytopes of Planar Point Sets
inferred← citeshttps://doi.org/10.1007/s00454-025-00783-wopenalex-snapshot
An Algorithm for Estimating the Crossing Number of Dense Graphs, and Continuous Analogs of the Crossing and Rectilinear Crossing Numbers
inferred← citeshttps://doi.org/10.1007/s10959-025-01426-9openalex-snapshot
Central Limit Theorem for Crossings in Randomly Embedded Graphs
inferred← citeshttps://doi.org/10.1007/s12650-020-00663-wopenalex-snapshot
Accelerating visual communication of mathematical knot deformation
inferred← citeshttps://doi.org/10.1016/j.comgeo.2017.06.015openalex-snapshot
Note on k-planar crossing numbers
inferred← citeshttps://doi.org/10.1016/j.comgeo.2019.04.003openalex-snapshot
Approximating the rectilinear crossing number
inferred← citeshttps://doi.org/10.1016/j.cosrev.2022.100490openalex-snapshot
Parameterized analysis and crossing minimization problems
inferred← citeshttps://doi.org/10.1016/j.dam.2022.07.027openalex-snapshot
The outerplanar crossing number of the complete bipartite graph
inferred← citeshttps://doi.org/10.1016/j.disc.2024.114288openalex-snapshot
Large matchings in maximal 1-planar graphs
inferred← citeshttps://doi.org/10.1016/j.jcss.2026.103777openalex-snapshot
Width notions for ordering-related problems
inferred← citeshttps://doi.org/10.1016/j.jcta.2017.04.003openalex-snapshot
The rectilinear local crossing number of K
inferred← citeshttps://doi.org/10.1016/j.jctb.2022.05.007openalex-snapshot
Crossings between non-homotopic edges
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An efficient metaheuristic for the K -page crossing number minimization problem
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A linear edge kernel for two-layer crossing minimization
inferred← citeshttps://doi.org/10.1016/j.tcs.2015.04.020openalex-snapshot
Fan-planarity: Properties and complexity
inferred← citeshttps://doi.org/10.1016/j.tcs.2025.115160openalex-snapshot
On 1-planar graphs with bounded cop-number
inferred← citeshttps://doi.org/10.1017/jpr.2025.10030openalex-snapshot
Limit theorems for the number of crossings and stress in projections of a random geometric graph
inferred← citeshttps://doi.org/10.1080/10556788.2023.2205646openalex-snapshot
Crossing edge minimization in radial outerplanar layered graphs using segment paths
inferred← citeshttps://doi.org/10.1103/physrevlett.133.077401openalex-snapshot
Measuring Entanglement in Physical Networks
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Mapping of Tourism Destinations by GIS-Blockchain RPCA based on PNPOLY Algorithm
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Synthetic Power Grids from Real World Models
inferred← citeshttps://doi.org/10.1111/cgf.15113openalex-snapshot
State of the Art of Graph Visualization in non‐Euclidean Spaces
inferred← citeshttps://doi.org/10.1137/1.9781611976465.165openalex-snapshot
2-Level Quasi-Planarity or How Caterpillars Climb (SPQR-)Trees
inferred← citeshttps://doi.org/10.1137/16m1062879openalex-snapshot
Structure of Graphs with Locally Restricted Crossings
inferred← citeshttps://doi.org/10.1137/17m1137231openalex-snapshot
Deciding Parity of Graph Crossing Number
inferred← citeshttps://doi.org/10.1142/s0218216520500431openalex-snapshot
Link crossing number is NP-hard
inferred← citeshttps://doi.org/10.1145/2714562openalex-snapshot
Layout-Aware Mixture Preparation of Biochemical Fluids on Application-Specific Digital Microfluidic Biochips
inferred← citeshttps://doi.org/10.1145/3301281openalex-snapshot
A Survey on Graph Drawing Beyond Planarity
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DoughNets: Visualising Networks Using Torus Wrapping
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Visually Communicating Mathematical Knot Deformation
inferred← citeshttps://doi.org/10.1145/3519935.3519984openalex-snapshot
A subpolynomial approximation algorithm for graph crossing number in low-degree graphs
inferred← citeshttps://doi.org/10.12677/aam.2023.122060openalex-snapshot
The Crossing Number of a Class of Transitive Decomposition Graphs
inferred← citeshttps://doi.org/10.1515/ms-2024-0079openalex-snapshot
The influence of separating cycles in drawings of K 5 ∖ e in the join product with paths and cycles
inferred← citeshttps://doi.org/10.2197/ipsjjip.25.542openalex-snapshot
On the Rectilinear Local Crossing Number of Km, n
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On plane subgraphs of complete topological drawings
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Cryptospatial Coordinate using the RPCA Based on a Point in Polygon Test for Cultural Heritage Tourism
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The worst graph layout algorithm ever
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The worst graph layout algorithm ever
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Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs
inferred← citeshttps://doi.org/10.3390/math12223484openalex-snapshot
Conjectures About Wheels Without One Edge with Paths and Cycles
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Strong Hanani-Tutte for the Torus
inferred← citeshttps://doi.org/10.48550/arxiv.1309.3665openalex-snapshot
Shellable drawings and the cylindrical crossing number of $K_n$
inferred← citeshttps://doi.org/10.48550/arxiv.1508.07926openalex-snapshot
The rectilinear local crossing number of $K_n$
inferred← citeshttps://doi.org/10.48550/arxiv.1606.03753openalex-snapshot
Approximating the rectilinear crossing number
inferred← citeshttps://doi.org/10.48550/arxiv.1702.05358openalex-snapshot
Computational topology of graphs on surfaces
inferred← citeshttps://doi.org/10.48550/arxiv.1807.11617openalex-snapshot
Tight Upper Bounds on the Crossing Number in a Minor-Closed Class
inferred← citeshttps://doi.org/10.48550/arxiv.1808.00385openalex-snapshot
A Note on the Maximum Rectilinear Crossing Number of Spiders
inferred← citeshttps://doi.org/10.48550/arxiv.1901.05155openalex-snapshot
A survey of graphs with known or bounded crossing numbers
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Embedded graphs : crossings and decompositions
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On the Maximum Crossing Number
inferred← citeshttps://doi.org/10.7155/jgaa.00534openalex-snapshot
Bundled Crossings Revisited
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An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
inferred← citeshttps://doi.org/10.7155/jgaa.00600openalex-snapshot
On the Maximum Number of Crossings in Star-Simple Drawings of $K_n$ with No Empty Lens
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Inserting Multiple Edges into a Planar Graph
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The crossing numbers of join products of four graphs of order five with paths and cycles
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