Isomorphism Testing for Graphs Excluding Small Minors

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