Isomorphism Testing for Graphs Excluding Small Minors

04/16/2020

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by   Martin Grohe, et al.

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