A Faster Isomorphism Test for Graphs of Small Degree

Abstract

In a recent breakthrough, Babai (STOC 2016) gave a quasipolynomial time graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithms runs in time $n^{O((\log d{)}^c)}$, where $n$ is the number of vertices of the input graphs, $d$ is the maximum degree of the input graphs, and $c$ is an absolute constant. The best previous isomorphism test for graphs of maximum degree $d$ due to Babai, Kantor and Luks (FOCS 1983) runs in time $n^{O(d/\log d)}$.

36 pages; second version significantly improves on the results and gives a faster isomorphism test for all graphs of maximum degree d rather than just graphs of maximum degree d and logarithmic diameter; third version adds additional explanations and corrects several typos