Isomorphism testing and canonical forms for k-contractable graphs (A generalization of bounded valence and bounded genus)

Abstract

This paper includes polynomial time isomorphism tests and canonical forms for graphs called k-contractable graphs for fixed k. The class of k-contractable graphs includes the graphs of bounded valence and the graphs of bounded genus. The algorithm uses several new ideas including: (1) it removes portions of the graph and replaces them with groups which are used to keep track of the symmetries of these portions; (2) it maintains with each group a tower of equivalence relation which allows a decomposition of the group. These towers are called a tower of Γk actions. It considers the canonical intersection of groups.