Isomorphism Testing for Graphs Excluding Small Minors

Abstract

We prove that there is a graph isomorphism test running in time on -vertex graphs excluding some -vertex graph as a minor. Previously known bounds were [I. N. Ponomarenko, J. Soviet Math., 55 (1991), pp. 1621–1643] and [L. Babai, Proceedings of the 48th Annual ACM Symposium on Theory of Computing, 2016, pp. 684–697]. For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.