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arXiv · 2004.07671

Isomorphism Testing for Graphs Excluding Small Minors

Martin Grohe·Daniel Neuen·Daniel Wiebking
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Abstract

We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.

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Martin Grohe, Daniel Neuen, Daniel Wiebking. 2020-04-16. Isomorphism Testing for Graphs Excluding Small Minors. https://doi.org/10.1137/21m1401930

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