Finding even cycles even faster

Abstract

We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: For every k ≥ 2, we can, in O(V2) time, decide whether an undirected graph G=(V, E) contains a simple cycle of length 2k and output such a cycle if it does. We can, again in O(V2) time, find a shortest even cycle in an undirected graph G=(V, E).