【摘要】 G是一个Kn-M图,M为完全图Kn中任意一个匹配.设σ2(G)表示不相邻顶点度和的最小值,令|V(G)|=n=∑ki=1ai,并且σ2(G)≥n+k-1.本文证明了对于图G中任意的k个顶点v1,v2,…,vk,存在点不相交的路P1,P2,…,Pk,使得对于1≤i≤k,都有|V(Pi)|=ai,并且vi是Pi的一个端点.更多还原

【Abstract】 G is a Kn-M graph,M is in complete graph Kn for any one match.Let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices.Let |V(G)|=n=∑ki=1ai,and suppose that σ2(G)≥n+k-1.It is proved that for any k vertices v1,v2,…,vk in G,there exist vertex disjoint paths P1,P2,…,Pk such that|V(Pi)|=ai,and vi is an end-vertex of Pi for1≤i≤k.更多还原