图是超级限制性边连通的一个Ore型充分条件

An Ore Type Sufficient Condition for a Graph to Be Super Restricted Edge-Connected

设 G是 n阶简单无向图 ,G的顶点 x的度记为 d(x) .证明了如果对 G中每一对不相邻的顶点 x和 y都有 d(x) +d(y)≥ n+2 ,那么 ,G是超级限制性边连通的 ,除非 n≥ 6是偶数且 G=2 Kn/2 ∪ F2 ,这里 F2 是 G的一个 2因子 .这一结果是对图的极大限制性边连通性的 Ore型充分条件的进一步扩展 .

Let G be a simple undirected graph of order n and d(x) denotes the degree of vertex x in G . The paper proved that if d(x)+d(y)≥n+2 for any pair of nonadjacent vertices x and y in G , then G is super restricted edge connected, unless n ≥6 is even and G =2 K n/2 ∪ F 2, where F 2 is a 2 factor of G . This result extends an Ore type sufficient condition for a graph to be maximally restricted edge connected.