Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjec...Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjectured that for any k independent edges e1,……, ek of G, G has a 2-factor with k cycles C1, C2, ……, Ck with respect to {e1, e2,……, ek} such that k - 1 of them are quadrilaterals. In this paper, we prove this conjecture.展开更多
基金NNSF of China(10471078)Higher Education of MOE,P.R.C.(2004042204)
文摘Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjectured that for any k independent edges e1,……, ek of G, G has a 2-factor with k cycles C1, C2, ……, Ck with respect to {e1, e2,……, ek} such that k - 1 of them are quadrilaterals. In this paper, we prove this conjecture.
