邻集交和点泛圈性质

Neighborhood Intersections and Vertex Pancyclicity

设G是阶为n(≥3),独立数α的简单图。本文证明了:如果对于G中任意不相邻点u,υ,都有|N(u)∩N(v)|≥α-1,则对于G的任一点x和任一整数k(4≤k≤n),G包含长度为k的圈经过x,除非一些特殊图。

Let G be a simple graph of order n with independence number a. It is proved in this paper that if, for any pair of nonadjacent vetrices u, v, |N(u) ∩ N (v)|≥a 1, then for any vertex x of G and any integer k(4≤k ≤n), G contains a cycle.of length k containing x unless G is in a special class of graphs.