Isomorphism Testing for Graphs Excluding Small Minors

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.