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.