Isomorphism Testing for Graphs Excluding Small Topological Subgraphs

11/30/2020

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by   Daniel Neuen, et al.

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We give an isomorphism test that runs in time n^polylog(h) on all n-vertex graphs excluding some h-vertex vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time n^polylog(n) (Babai, STOC 2016) and n^f(h) for some function f (Grohe and Marx, SIAM J. Comp., 2015). Our result also unifies and extends previous isomorphism tests for graphs of maximum degree d running in time n^polylog(d) (FOCS 2018) and for graphs of Hadwiger number h running in time n^polylog(h) (FOCS 2020).