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The Thickness of Graphs: A Survey

https://doi.org/10.1007/pl00007219
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-10704-5_9openalex-snapshot
A graph-planarization algorithm and its application to random graphs
inferredcites →https://doi.org/10.1007/3-540-50728-0_56openalex-snapshot
O(n2) algorithms for graph planarization
inferredcites →https://doi.org/10.1007/bf01759038openalex-snapshot
Multilayer grid embeddings for VLSI
inferredcites →https://doi.org/10.1016/0012-365x(87)90195-6openalex-snapshot
A construction of thickness-minimal graphs
inferredcites →https://doi.org/10.1016/0020-0255(91)90052-vopenalex-snapshot
On the thickness of graphs of given degree
inferredcites →https://doi.org/10.1016/0095-8956(71)90065-7openalex-snapshot
Graphs with forbidden subgraphs
inferredcites →https://doi.org/10.1016/0095-8956(72)90010-xopenalex-snapshot
Décomposition de K16 en Trois Graphes Planaires
inferredcites →https://doi.org/10.1016/0095-8956(87)90004-9openalex-snapshot
On the genus and thickness of graphs
inferredcites →https://doi.org/10.1016/0095-8956(91)90100-xopenalex-snapshot
On the thickness and arboricity of a graph
inferredcites →https://doi.org/10.1016/s0022-0000(76)80045-1openalex-snapshot
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
inferredcites →https://doi.org/10.1016/s0166-218x(96)00029-7openalex-snapshot
Rectangle-visibility representations of bipartite graphs
inferredcites →https://doi.org/10.1016/s0925-7721(99)00018-8openalex-snapshot
On representations of some thickness-two graphs
inferredcites →https://doi.org/10.1016/s1385-7258(63)50055-9openalex-snapshot
The thickness of a graph
inferredcites →https://doi.org/10.1017/cbo9780511662072.010openalex-snapshot
Outerthickness and outercoarseness of graphs
inferredcites →https://doi.org/10.1017/s0305004100037385openalex-snapshot
On the thickness of the complete bipartite graph
inferredcites →https://doi.org/10.1017/s030500410006028xopenalex-snapshot
Determining the thickness of graphs is NP-hard
inferredcites →https://doi.org/10.1049/ip-e.1992.0021openalex-snapshot
Embedding graphs in books: a survey
inferredcites →https://doi.org/10.1070/sm1976v030n02abeh002267openalex-snapshot
THE THICKNESS OF AN ARBITRARY COMPLETE GRAPH
inferredcites →https://doi.org/10.1090/s0002-9904-1962-10850-7openalex-snapshot
Every planar graph with nine points has a nonplanar complement
inferredcites →https://doi.org/10.1109/43.21845openalex-snapshot
O(n/sup 2/) algorithms for graph planarization
inferredcites →https://doi.org/10.1109/90.222924openalex-snapshot
Scheduling algorithms for multihop radio networks
inferredcites →https://doi.org/10.1109/tcs.1977.1084323openalex-snapshot
Thickness of graphs with degree constrained vertices
inferredcites →https://doi.org/10.1112/jlms/s1-36.1.445openalex-snapshot
Edge-Disjoint Spanning Trees of Finite Graphs
inferredcites →https://doi.org/10.1137/0222068openalex-snapshot
An $O(m\log n)$-Time Algorithm for the Maximal Planar Subgraph Problem
inferredcites →https://doi.org/10.1145/321850.321852openalex-snapshot
Efficient Planarity Testing
inferredcites →https://doi.org/10.4153/cjm-1965-084-2openalex-snapshot
The Thickness of the Complete Graph
inferredcites →https://doi.org/10.4153/cjm-1969-109-4openalex-snapshot
Minimal Decompositions of Complete Graphs into Subgraphs with Embeddability Properties
inferredcites →https://doi.org/10.4153/cmb-1963-026-xopenalex-snapshot
The Non-Biplanar Character of the Complete 9-Graph
inferredcites →https://doi.org/10.4153/cmb-1968-088-xopenalex-snapshot
Note on T-Minimal Complete Bipartite Graphs
inferredcites →https://doi.org/10.6028/jres.072b.023openalex-snapshot
Thickness and connectivity in graphs

What points at this work

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

inferred← citeshttps://doi.org/10.1002/jcd.21665openalex-snapshot
Using block designs in crossing number bounds
inferred← citeshttps://doi.org/10.1002/jgt.23273openalex-snapshot
Spanning Plane Subgraphs of 1‐Plane Graphs
inferred← citeshttps://doi.org/10.1002/rsa.20221openalex-snapshot
Biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method
inferred← citeshttps://doi.org/10.1007/11618058_13openalex-snapshot
Graph Treewidth and Geometric Thickness Parameters
inferred← citeshttps://doi.org/10.1007/11618058_21openalex-snapshot
Non-planar Core Reduction of Graphs
inferred← citeshttps://doi.org/10.1007/11785293_25openalex-snapshot
Simultaneous Embedding with Two Bends per Edge in Polynomial Area
inferred← citeshttps://doi.org/10.1007/3-540-36379-3_34openalex-snapshot
Two Counterexamples in Graph Drawing
inferred← citeshttps://doi.org/10.1007/978-3-030-39219-2_36openalex-snapshot
Planar Projections of Graphs
inferred← citeshttps://doi.org/10.1007/978-3-030-68766-3_3openalex-snapshot
The Local Queue Number of Graphs with Bounded Treewidth
inferred← citeshttps://doi.org/10.1007/978-3-031-22203-0_18openalex-snapshot
The Thickness of Fan-Planar Graphs is At Most Three
inferred← citeshttps://doi.org/10.1007/978-3-031-49272-3_8openalex-snapshot
Minimizing an Uncrossed Collection of Drawings
inferred← citeshttps://doi.org/10.1007/978-3-031-82670-2_16openalex-snapshot
Pathways to Tractability for Geometric Thickness
inferred← citeshttps://doi.org/10.1007/978-3-319-27261-0_17openalex-snapshot
Maximizing the Degree of (Geometric) Thickness-t Regular Graphs
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/10.1007/978-3-540-30559-0_32openalex-snapshot
The Hypocoloring Problem: Complexity and Approximability Results when the Chromatic Number Is Small
inferred← citeshttps://doi.org/10.1007/978-3-540-31843-9_21openalex-snapshot
Simultaneous Embedding of Planar Graphs with Few Bends
inferred← citeshttps://doi.org/10.1007/978-3-540-32439-3_4openalex-snapshot
Biplanar Crossing Numbers I: A Survey of Results and Problems
inferred← citeshttps://doi.org/10.1007/978-3-540-45078-8_22openalex-snapshot
On Simultaneous Planar Graph Embeddings
inferred← citeshttps://doi.org/10.1007/978-3-540-70904-6_32openalex-snapshot
Thickness of Bar 1-Visibility Graphs
inferred← citeshttps://doi.org/10.1007/978-3-540-74456-6_36openalex-snapshot
Packing and Squeezing Subgraphs into Planar Graphs
inferred← citeshttps://doi.org/10.1007/978-3-642-00219-9_6openalex-snapshot
Cubic Graphs Have Bounded Slope Parameter
inferred← citeshttps://doi.org/10.1007/978-3-642-25878-7_25openalex-snapshot
Drawing Cubic Graphs with the Four Basic Slopes
inferred← citeshttps://doi.org/10.1007/978-3-642-40104-6_31openalex-snapshot
Planar Packing of Binary Trees
inferred← citeshttps://doi.org/10.1007/978-3-642-45043-3_21openalex-snapshot
Thickness and Colorability of Geometric Graphs
inferred← citeshttps://doi.org/10.1007/s00453-012-9680-0openalex-snapshot
The Complexity of the Empire Colouring Problem
inferred← citeshttps://doi.org/10.1007/s00453-025-01351-7openalex-snapshot
Geometric Thickness of Multigraphs is $$\exists \mathbb {R}$$-Complete
inferred← citeshttps://doi.org/10.1007/s00454-007-1318-7openalex-snapshot
Graph Treewidth and Geometric Thickness Parameters
inferred← citeshttps://doi.org/10.1007/s00493-018-3733-1openalex-snapshot
Defective Colouring of Graphs Excluding A Subgraph or Minor
inferred← citeshttps://doi.org/10.1007/s10255-024-1128-1openalex-snapshot
The Thickness of Some Complete Bipartite and Tripartite Graphs
inferred← citeshttps://doi.org/10.1007/s10732-005-6999-6openalex-snapshot
Heuristics for the Maximum Outerplanar Subgraph Problem
inferred← citeshttps://doi.org/10.1007/s10878-016-0057-1openalex-snapshot
The thickness of the complete multipartite graphs and the join of graphs
inferred← citeshttps://doi.org/10.1007/s11401-026-0003-1openalex-snapshot
The Arboricity of Graphs with Minimum Genus Embeddings
inferred← citeshttps://doi.org/10.1016/j.akcej.2019.05.004openalex-snapshot
The 6-girth-thickness of the complete graph
inferred← citeshttps://doi.org/10.1016/j.comgeo.2006.05.006openalex-snapshot
On simultaneous planar graph embeddings
inferred← citeshttps://doi.org/10.1016/j.comgeo.2008.05.003openalex-snapshot
Simultaneous graph embedding with bends and circular arcs
inferred← citeshttps://doi.org/10.1016/j.comgeo.2010.09.005openalex-snapshot
On graph thickness, geometric thickness, and separator theorems
inferred← citeshttps://doi.org/10.1016/j.comgeo.2016.03.003openalex-snapshot
Thickness and colorability of geometric graphs
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.2023.102036openalex-snapshot
Straight-line drawings of 1-planar graphs
inferred← citeshttps://doi.org/10.1016/j.dam.2004.06.016openalex-snapshot
A hypocoloring model for batch scheduling
inferred← citeshttps://doi.org/10.1016/j.dam.2021.08.015openalex-snapshot
Planar projections of graphs
inferred← citeshttps://doi.org/10.1016/j.dam.2025.06.061openalex-snapshot
On the biplanar and k -planar crossing numbers
inferred← citeshttps://doi.org/10.1016/j.dam.2025.07.025openalex-snapshot
The thickness of a graph with constraint on girth
inferred← citeshttps://doi.org/10.1016/j.disc.2007.05.007openalex-snapshot
Planarization and fragmentability of some classes of graphs
inferred← citeshttps://doi.org/10.1016/j.disc.2007.12.078openalex-snapshot
Non-planar core reduction of graphs
inferred← citeshttps://doi.org/10.1016/j.disc.2015.10.023openalex-snapshot
Three ways to cover a graph
inferred← citeshttps://doi.org/10.1016/j.disc.2018.02.003openalex-snapshot
Local and union boxicity
inferred← citeshttps://doi.org/10.1016/j.disc.2018.02.024openalex-snapshot
Thickness and outerthickness for embedded graphs
inferred← citeshttps://doi.org/10.1016/j.ejc.2017.05.010openalex-snapshot
The k -strong induced arboricity of a graph
inferred← citeshttps://doi.org/10.1016/j.ins.2003.06.008openalex-snapshot
A note on Halton's conjecture
inferred← citeshttps://doi.org/10.1016/j.ins.2004.02.029openalex-snapshot
A simulated annealing algorithm for determining the thickness of a graph
inferred← citeshttps://doi.org/10.1016/s0012-365x(03)00240-1openalex-snapshot
Geometric thickness in a grid
inferred← citeshttps://doi.org/10.1016/s0020-0190(02)00432-5openalex-snapshot
Worst case analysis of a greedy algorithm for graph thickness
inferred← citeshttps://doi.org/10.1016/s0020-0255(01)00126-8openalex-snapshot
A genetic algorithm for determining the thickness of a graph
inferred← citeshttps://doi.org/10.1016/s1571-0653(04)00413-5openalex-snapshot
Geometric Thickness in a Grid of Linear Area
inferred← citeshttps://doi.org/10.1017/s0963548319000063openalex-snapshot
Defective and clustered choosability of sparse graphs
inferred← citeshttps://doi.org/10.1023/a:1021616706461openalex-snapshot
An Efficient Algorithm for Embedding Nonplanar Graphs in Planes
inferred← citeshttps://doi.org/10.1038/s41586-024-07107-7openalex-snapshot
High-threshold and low-overhead fault-tolerant quantum memory
inferred← citeshttps://doi.org/10.1080/00207160410001684352openalex-snapshot
A simulated annealing algorithm for the maximum planar subgraph problem
inferred← citeshttps://doi.org/10.1093/comjnl/bxw075openalex-snapshot
Area-Thickness Trade-Offs for Straight-Line Drawings of Planar Graphs
inferred← citeshttps://doi.org/10.1103/physrevlett.129.050504openalex-snapshot
Constant-Overhead Quantum Error Correction with Thin Planar Connectivity
inferred← citeshttps://doi.org/10.1109/glocom.2007.143openalex-snapshot
On High Spatial Reuse Link Scheduling in STDMA Wireless Ad Hoc Networks
inferred← citeshttps://doi.org/10.1137/22m1542854openalex-snapshot
Treewidth, Circle Graphs, and Circular Drawings
inferred← citeshttps://doi.org/10.1145/1060590.1060666openalex-snapshot
Edge partition of planar sraphs into two outerplanar graphs
inferred← citeshttps://doi.org/10.1145/2543581.2543589openalex-snapshot
Unsolved problems in visibility graphs of points, segments, and polygons
inferred← citeshttps://doi.org/10.1145/997817.997868openalex-snapshot
The geometric thickness of low degree graphs
inferred← citeshttps://doi.org/10.17877/de290r-367openalex-snapshot
Computing crossing numbers
inferred← citeshttps://doi.org/10.20382/jocg.v9i1a12openalex-snapshot
Thickness and Antithickness of Graphs
inferred← citeshttps://doi.org/10.26493/1855-3974.1236.4d7openalex-snapshot
A note on the thickness of some complete bipartite graphs
inferred← citeshttps://doi.org/10.26493/1855-3974.1349.b67openalex-snapshot
The 4-girth-thickness of the complete graph
inferred← citeshttps://doi.org/10.26493/1855-3974.1998.2f4openalex-snapshot
The thickness of the Kronecker product of graphs
inferred← citeshttps://doi.org/10.26493/1855-3974.823.068openalex-snapshot
Remarks on the thickness of K_n,n,n
inferred← citeshttps://doi.org/10.35834/mjms/1337950501openalex-snapshot
An Annotated Bibliography on the Thickness, Outerthickness, and Arboricity of a Graph
inferred← citeshttps://doi.org/10.37236/1029openalex-snapshot
Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness
inferred← citeshttps://doi.org/10.37236/1141openalex-snapshot
A Note on the Number of Hamiltonian Paths in Strong Tournaments
inferred← citeshttps://doi.org/10.37236/7406openalex-snapshot
Defective and Clustered Graph Colouring
inferred← citeshttps://doi.org/10.4086/cjtcs.2016.001openalex-snapshot
inferred← citeshttps://doi.org/10.4153/cmb-2016-020-1openalex-snapshot
The Thickness of the Cartesian Product of Two Graphs
inferred← citeshttps://doi.org/10.48550/arxiv.0812.4744openalex-snapshot
On Wireless Link Scheduling and Flow Control
inferred← citeshttps://doi.org/10.48550/arxiv.1009.4641openalex-snapshot
Decomposition of Geometric Set Systems and Graphs
inferred← citeshttps://doi.org/10.48550/arxiv.1012.5187openalex-snapshot
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
inferred← citeshttps://doi.org/10.48550/arxiv.1106.1973openalex-snapshot
Drawing cubic graphs with the four basic slopes
inferred← citeshttps://doi.org/10.48550/arxiv.1204.5853openalex-snapshot
Simultaneous Embedding of Planar Graphs
inferred← citeshttps://doi.org/10.48550/arxiv.1607.07174openalex-snapshot
The $k$-strong induced arboricity of a graph
inferred← citeshttps://doi.org/10.48550/arxiv.1911.06403openalex-snapshot
New Bounds on the Biplanar and $k$-Planar Crossing Numbers
inferred← citeshttps://doi.org/10.48550/arxiv.math/0109195openalex-snapshot
Separating Geometric Thickness from Book Thickness
inferred← citeshttps://doi.org/10.51408/csit2023_33openalex-snapshot
On Interval Coloring Thickness of Some Classes of Bipartite Graphs
inferred← citeshttps://doi.org/10.5614/ejgta.2019.7.1.14openalex-snapshot
The 4-girth-thickness of the complete multipartite graph
inferred← citeshttps://doi.org/10.7151/dmgt.1942openalex-snapshot
The thickness of amalgamations and Cartesian product of graphs
inferred← citeshttps://doi.org/10.7155/jgaa.00032openalex-snapshot
Planarizing Graphs - A Survey and Annotated Bibliography
inferred← citeshttps://doi.org/10.7155/jgaa.00113openalex-snapshot
Simultaneous Embedding of Planar Graphs with Few Bends
inferred← citeshttps://doi.org/10.7155/jgaa.00157openalex-snapshot
Parameters of Bar k-Visibility Graphs
inferred← citeshttps://doi.org/10.7155/jgaa.00196openalex-snapshot
Cubic graphs have bounded slope parameter
inferred← citeshttps://doi.org/10.7155/jgaa.00362openalex-snapshot
On k-visibility graphs
inferred← citeshttps://doi.org/10.7282/t3xd10qdopenalex-snapshot
Obstacles, slopes and tic-tac-toe
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