【摘要】 论证了对整数ｎ（ｎ≥３）和ｋ（ｋ≥２），若ｋ为奇数，则令ｋ≥ｎ－１，Ｇ是一个不含Ｋ１，ｎ的２边连通图，ｋ｜Ｖ（Ｇ）｜≡ｏ（ｍｏｄ２），设Ｇ的顶点最小度α（Ｇ）至少为（ｎ２／４（ｎ－１））ｋ＋（３ｎ－６）／２＋（ｎ－１）／４ｋ，则Ｇ是ｋ覆盖图．并且说明了定理中条件“２边连通”不能减弱为“连通”．更多还原

【Abstract】 Proved the following theorem: let n(n ≥3) and k,(k ≥2) be positive integers. If k is odd, we assume that k ≥ n -1. Let G be a 2 edge connected K 1,n free graph with k|V(G) | even, and suppose that the minimum degree of G is at least (n 2/4(n-1))k+(3n-6)/2+(n-1)/4k . Then G is a k covered graph. We also show that the condition " 2 edge connected" in this theorem cannot be dropped.更多还原