一个关于图是[a,b;n]-均匀的度条件

The Degree Conditions for Graphs to be[a,b;n]-uniform Graphs

设t,a,b和n为整数且1≤a<b,t≥3以及n≥1.如果G的导出子图不含有K_(1,t),则该图G称为K_(1,t-)无爪图.如果对于图G中含有n条边的任意匹配M,都在G中有[a,b]-因子F包含M以及在G中有另一个[a,b]-因子F′不包含M,则图G称为[a,b;n]-均匀图.给出了K_(1,t-)无星图G是[a,b;n]-均匀图的度条件.进一步,指出本文中的结果在某种意义上说是最佳的.

Let t,a,b and n be integers with l≤a6,t≥3 and n≥1.A graph G is called K1,t-free if G contains no K1,t as an induced subgraph.A graph G is called[a,b;n]-uniform graph if for any matching M with n edges of G,there is an[a,b]-factor F of G containing M and there is another[a,b]-factor F＇ of G excluding M.The degree conditions for K1,t-free graph G to be an[a,b;n]-uniform graph are given.Furthermore,it is shown that many results in this paper are sharp in some sense.