Isomorphism Testing for Graphs Excluding Small Topological Subgraphs
Daniel Neuen

TL;DR
This paper presents a new isomorphism testing algorithm for graphs excluding certain small topological subgraphs, achieving faster runtimes than previous methods for specific graph classes.
Contribution
It introduces an isomorphism test with runtime $n^{ ext{polylog}(h)}$ for graphs excluding a fixed $h$-vertex topological subgraph, unifying and extending prior results.
Findings
Runs in time $n^{ ext{polylog}(h)}$ for excluded topological subgraphs
Unifies previous algorithms for bounded degree and Hadwiger number graphs
Improves efficiency over prior isomorphism tests for specific graph classes
Abstract
We give an isomorphism test that runs in time on all -vertex graphs excluding some -vertex vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time (Babai, STOC 2016) and for some function (Grohe and Marx, SIAM J. Comp., 2015). Our result also unifies and extends previous isomorphism tests for graphs of maximum degree running in time (SIAM J. Comp., 2023) and for graphs of Hadwiger number running in time (SIAM J. Comp., 2023).
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Machine Learning and Algorithms · Advanced Graph Theory Research
