无爪图成为哈米顿的一个充分条件

A Sufficient Condition for Claw-Free Graphs to be Hamiltonian

本文给出下列定理:设G是阶为n≥3的2-连通无爪图,如果对每对不同的非邻顶点x,y有不等式2|N(x)UN(y)|+d(x)+d(y)≥2n-5成立,则G是哈米顿的.

In this paper, we present the following theorem: let G be a 2-con nected, claw-free graph of order n≥3. For each pair of distinct nonadjacent vertices x, y, if the inequality 2 |N(x) ∪ N(y)|+d(x) + d(y)≥ 2n - 5 holds, then G is Hamiltonian.