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The Weisfeiler--Leman Dimension of Planar Graphs Is at Most 3

https://doi.org/10.1145/3333003
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What this work says

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

inferredcites →https://doi.org/10.1007/11786986_2openalex-snapshot
Testing Graph Isomorphism in Parallel by Playing a Game
inferredcites →https://doi.org/10.1007/3-540-49257-7_6openalex-snapshot
Definability and Descriptive Complexity on Databases of Bounded Tree-Width
inferredcites →https://doi.org/10.1007/978-3-319-06686-8_21openalex-snapshot
Dynamic Complexity of Planar 3-Connected Graph Isomorphism
inferredcites →https://doi.org/10.1007/978-3-319-22177-9_26openalex-snapshot
On the Power of Color Refinement
inferredcites →https://doi.org/10.1007/978-3-662-48057-1_25openalex-snapshot
Graphs Identified by Logics with Counting
inferredcites →https://doi.org/10.1007/bf01098279openalex-snapshot
The isomorphism problem for classes of graphs closed under contraction
inferredcites →https://doi.org/10.1007/bf01305232openalex-snapshot
An optimal lower bound on the number of variables for graph identification
inferredcites →https://doi.org/10.1016/0020-0190(71)90019-6openalex-snapshot
A V2 algorithm for determining isomorphism of planar graphs
inferredcites →https://doi.org/10.1016/j.jsc.2013.09.003openalex-snapshot
Practical graph isomorphism, II
inferredcites →https://doi.org/10.1016/s0022-0000(73)80013-3openalex-snapshot
A V log V algorithm for isomorphism of triconnected planar graphs
inferredcites →https://doi.org/10.1017/9781139028868openalex-snapshot
Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
inferredcites →https://doi.org/10.1023/a:1021146226285openalex-snapshot
On the Structure of a k-Connected Graph
inferredcites →https://doi.org/10.1108/ir.1999.04926fae.001openalex-snapshot
Lecture Notes in Computer Science 1205
inferredcites →https://doi.org/10.1109/ccc.2009.16openalex-snapshot
Planar Graph Isomorphism is in Log-Space
inferredcites →https://doi.org/10.1109/lics.1998.705639openalex-snapshot
Fixed-point logics on planar graphs
inferredcites →https://doi.org/10.1112/plms/s3-13.1.743openalex-snapshot
How to Draw a Graph
inferredcites →https://doi.org/10.1137/120867834openalex-snapshot
Sherali--Adams Relaxations and Indistinguishability in Counting Logics
inferredcites →https://doi.org/10.1145/2371656.2371662openalex-snapshot
Fixed-point definability and polynomial time on graphs with excluded minors
inferredcites →https://doi.org/10.1145/2933575.2933595openalex-snapshot
Upper Bounds on the Quantifier Depth for Graph Differentiation in First Order Logic
inferredcites →https://doi.org/10.1145/2933575.2934560openalex-snapshot
Near-Optimal Lower Bounds on Quantifier Depth and Weisfeiler--Leman Refinement Steps
inferredcites →https://doi.org/10.1145/335305.335313openalex-snapshot
Isomorphism testing for embeddable graphs through definability
inferredcites →https://doi.org/10.1201/b15385openalex-snapshot
Handbook of Graph Drawing and Visualization
inferredcites →https://doi.org/10.4230/dagrep.5.12.1openalex-snapshot
The Graph Isomorphism Problem (Dagstuhl Seminar 15511)
inferredcites →https://doi.org/10.7155/jgaa.00232openalex-snapshot
Recursive generation of simple planar 5-regular graphs and pentangulations

What points at this work

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

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The Weisfeiler-Leman Algorithm and Recognition of Graph Properties
inferred← citeshttps://doi.org/10.1007/978-3-031-20350-3_15openalex-snapshot
Circle Graph Isomorphism in Almost Linear Time
inferred← citeshttps://doi.org/10.1007/978-3-031-43587-4_17openalex-snapshot
On the Parallel Complexity of Group Isomorphism via Weisfeiler–Leman
inferred← citeshttps://doi.org/10.1007/978-981-97-0566-5_23openalex-snapshot
Canonization of a Random Circulant Graph by Counting Walks
inferred← citeshttps://doi.org/10.1007/s00010-022-00902-5openalex-snapshot
On polyhedral graphs and their complements
inferred← citeshttps://doi.org/10.1007/s00373-020-02206-4openalex-snapshot
Separability of Schur Rings Over Abelian Groups of Odd Order
inferred← citeshttps://doi.org/10.1007/s00373-021-02308-7openalex-snapshot
The Weisfeiler–Leman Dimension of Chordal Bipartite Graphs Without Bipartite Claw
inferred← citeshttps://doi.org/10.1007/s00373-023-02683-3openalex-snapshot
The Weisfeiler–Leman Dimension of Distance-Hereditary Graphs
inferred← citeshttps://doi.org/10.1016/j.cosrev.2026.100918openalex-snapshot
Parameterized complexity of graph isomorphism testing
inferred← citeshttps://doi.org/10.1016/j.disc.2021.112692openalex-snapshot
On WL-rank of Deza Cayley graphs
inferred← citeshttps://doi.org/10.1016/j.disc.2025.114526openalex-snapshot
Cartesian products of graphs and their coherent configurations
inferred← citeshttps://doi.org/10.1016/j.jcss.2025.103703openalex-snapshot
On the parallel complexity of group isomorphism via Weisfeiler–Leman
inferred← citeshttps://doi.org/10.1017/9781009036214.006openalex-snapshot
Recent advances on the graph isomorphism problem
inferred← citeshttps://doi.org/10.1017/s096354832510028xopenalex-snapshot
Canonization of a random circulant graph by counting walks
inferred← citeshttps://doi.org/10.1038/s41540-026-00804-1openalex-snapshot
A controlled in silico benchmark for GNN prediction of tissue dynamics
inferred← citeshttps://doi.org/10.1109/lics.2019.8785682openalex-snapshot
Canonisation and Definability for Graphs of Bounded Rank Width
inferred← citeshttps://doi.org/10.1109/lics56636.2023.10175818openalex-snapshot
Simulating Logspace-Recursion with Logarithmic Quantifier Depth
inferred← citeshttps://doi.org/10.1109/tkde.2025.3552045openalex-snapshot
Multiscale Weisfeiler-Leman Directed Graph Neural Networks for Prerequisite-Link Prediction
inferred← citeshttps://doi.org/10.1137/1.9781611977073.59openalex-snapshot
Isomorphism Testing for Graphs Excluding Small Topological Subgraphs
inferred← citeshttps://doi.org/10.1137/20m1314987openalex-snapshot
The Power of the Weisfeiler--Leman Algorithm to Decompose Graphs
inferred← citeshttps://doi.org/10.1137/23m1575019openalex-snapshot
On the Weisfeiler–Leman Dimension of Permutation Graphs
inferred← citeshttps://doi.org/10.1137/23m1603522openalex-snapshot
Faster Isomorphism for \({p}\)-Groups of Class 2 and Exponent \({p}\)
inferred← citeshttps://doi.org/10.1142/s0218196724500103openalex-snapshot
Count-free Weisfeiler–Leman and group isomorphism
inferred← citeshttps://doi.org/10.1142/s100538672100033xopenalex-snapshot
On Separable Schur Rings over Abelian Groups
inferred← citeshttps://doi.org/10.1145/3373718.3394786openalex-snapshot
On the Weisfeiler-Leman Dimension of Finite Groups
inferred← citeshttps://doi.org/10.1145/3436980.3436982openalex-snapshot
The Weisfeiler-Leman algorithm
inferred← citeshttps://doi.org/10.1145/3564246.3585250openalex-snapshot
Faster Isomorphism for 𝑝-Groups of Class 2 and Exponent 𝑝
inferred← citeshttps://doi.org/10.1145/3568025openalex-snapshot
Canonisation and Definability for Graphs of Bounded Rank Width
inferred← citeshttps://doi.org/10.1145/3651614openalex-snapshot
Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-Complexity
inferred← citeshttps://doi.org/10.1145/3651986openalex-snapshot
Isomorphism Testing for Graphs Excluding Small Topological Subgraphs
inferred← citeshttps://doi.org/10.1145/3661814.3662122openalex-snapshot
Bounding the Weisfeiler-Leman Dimension via a Depth Analysis of I/R-Trees
inferred← citeshttps://doi.org/10.1145/3677121openalex-snapshot
Cutting Planes Width and the Complexity of Graph Isomorphism Refutations
inferred← citeshttps://doi.org/10.1145/3771726openalex-snapshot
Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-Complexity
inferred← citeshttps://doi.org/10.1145/3798282openalex-snapshot
Computational Complexity of the Weisfeiler-Leman Dimension
inferred← citeshttps://doi.org/10.18154/rwth-2022-01183openalex-snapshot
Weisfeiler-Leman, Graph Spectra, and Random Walks
inferred← citeshttps://doi.org/10.2139/ssrn.5359303openalex-snapshot
Towards Efficient and Scalable Graph Neural Architectures for Large-Scale Systems
inferred← citeshttps://doi.org/10.24963/ijcai.2021/291openalex-snapshot
The Surprising Power of Graph Neural Networks with Random Node Initialization
inferred← citeshttps://doi.org/10.4204/eptcs.390.12openalex-snapshot
On the Descriptive Complexity of Groups without Abelian Normal Subgroups (Extended Abstract)
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