VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

H. Wang considered the minimum degrees condition that G has large vertex-disjoint cycles in bipartite graphs. Motivated by this, we consider the small vertex-disjoint cycles in bipartite graphs in this paper. We prove the following result: Let m > 3, n > 2 and k >1 be three integers. Let G = (V1,V2;E) be a bipartite graph with | V1| = | V2| =n > 2k+1. If the minimum degreefor any cycle C of G with length 2m, then G contains k vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp.