Hamilton无爪图的一个充分条件

A SUFFICIENT CONDITION FOR HAMILTON CLAW FREE GRAPHS

设Ｇ是阶为ｎ（≥３），连通度为ｋ的简单无爪图，证明了如果对每一个阶为ｋ＋１的独立集Ｓ中的每一对点ｕ、ｖ，都有｜Ｎ（ｕ）∪Ｎ（ｖ）｜≥ｎ－ｋ－Δ（Ｓ）。

On the assumption that G is a claw free graph of order n (≥3) and connectivity k , it is proved that G is a Hamilton graph if for any distinct vertices u and v in any independent set S of cardinality k+1 , |N(v)∪N(V)|≥n-k- Δ (S) .