A degree condition of 2-factors in bipartite graphs

Let G = (V-1, V-2;E) be a bipartite graph with /V-1/ = /V-2/ = n, and sigma (2)(G) = min{d(u) + d(v): u, v is an element of V(G), uv is not an element of (G)}. In this paper, we show that G has a 2-factor which exactly contai ns k independent cycles if sigma (2)(G) greater than or equal to n + 2 for any 1 less than or equal to k less than or equal to [(n - 1)/2], and we als o show that the result is sharp. (C) 2001 Published by Elsevier Science B.V .