Canonical labelling of graphs in linear average time

Abstract

Canonical labelling of graphs (CL, for short) can be used, e.g., to test isomorphism. We prove that a simple vertex classification procedure results after only two refinement steps in a CL of random graphs with probability 1 - exp(-cn). With a slight modification we obtain a linear time CL algorithm with only exp(-cn log n/log log n) probability of failure. An additional depth-first search yields a CL of all graphs in linear average time.