关于Win猜想的两个结果
Two Results on Win's Conjecture
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摘要: 设G是2n个顶点的简单图,k为不小于-1的整数,若G中每一对不相邻的顶点u和v,都有d(u)+d(v)≥2n+k,则称G为Ore k-型图。S.Win1给出下面的猜想:若G是Ore k-型图,则G有k+2个边不相交的1-因子。其中k≤2n-4。本文证明了k=2n-4和k=2n-5时Win猜想是成立的。Abstract: Let G be a simple graph on 2n vertices and k an integer satisfying -1≤k, If d(u)+d(v)≥2n+k for every two nonadjacent verfices u and v of the graph G, then G is said to be the graph of Ore-type-(k). S. Win1 gave the folloing conjecture:If G is the graph Ore-type-(k), then G contains k+2 disjoint 1-factors, where k≤2n-4.In this paper, we proved that Win's conjecture is tre for k=2n-4, 2u-5.
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