均衡二分图中含有大圈的2-因子的度和条件

A Degree Sum Condition of 2-factors with Large Cycles in Balanced Bipartite Graphs

设G=(V1,V2;E)是一个二分图,满|V1|=|V2|=n sk+1足,其中s 4,k 1是两个正整数.定义G中不相邻两点的最小度和为σ2(G)=min{dG(u)+dG(v)∶u,v∈V(G),uv E(G)}.在这篇文章中,我们证明了如果σ2(G)2「(1-1s)n﹁+2。

Let G=（V1,V2;E） be a bipartite graph with ｜V1｜= ｜V2｜=n≥sk＋1,where s≥4 and k≥l are two integers. We define the minimum degree sum of nonadjacent vertices of graph G to be σ2（G）=min{dG（u）＋dG（v）：u,v∈V（G）,uv∈E（G）}. In this paper, we will prove that if σ2（G）≥2r（1-1/s）n]＋2 then G has a 2 - factor with s exactly k vertex-disjoint cycles of length at least 2s.