We describe efficient algorithms for finding even cycles in undirected
graphs. Our main results are the following: (i) For every k greater t
han or equal to 2, there is an O(V-2) time algorithm that decides whet
her an undirected graph G = (V, E) contains a simple cycle of length 2
k, and finds one if it does. (ii) There is an O(V-2) time algorithm th
at finds a shortest even cycle in an undirected graph G = (V, E).