Decomposition of Km,n into short cycles Original Research Article

Let Km,n be the complete bipartite graph and Cr be an elementary cycle of length r. In this paper, it is shown that G can be decomposed into p copies of C4, q copies of C6 and r copies of C8 for each triple p,q,r of nonnegative integers such that 4p + 6q + 8r = |E(G)|, in the following two cases: 1. (a) G = Km,n, if m ⩾ 4, n ⩾ 6, and m, n are even 2. (b) G = Km,n minus a 1-factor, if n is odd.