Abstract
Liu and Yan gave the degree condition for a balanced bipartite graph G = (V 1, V 2;E) to have k vertex–disjoint quadrilaterals containing any given k independent edges e 1, . . . , e k of G, respectively. They also conjectured that for any k independent edges e 1, . . . , e k of G, G has a 2–factor with k cycles C 1,C 2, . . . , C k with respect to {e 1, e 2, . . . , e k } such that k–1 of them are quadrilaterals. In this paper, we prove this conjecture.
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