Finding Cycles of a Given Length

We present an O(n 2 ) algorithm to find a cycle of length 4 in G if one exists and an O(n k · K 5/2 ) algorithm to find a cycle of length 2k(k ≥ 3) in G if one exists. The latter algorithm may be modified to obtain an O(n k+1 · k 5/2 ) algorithm to find a cycle of length 2k + 1 (k ≥ 2) in G if one exists.