连通、P_3-局部连通[5,3]-图的圈可扩性

Cycle extendability of connected and P_3-locally connected [5,3]-graphs

如果图G的任意s个顶点的导出子图中至少含有t条边,则称G为[s,t]-图。设H是一个图,如果图G中任意一个同构于H的子图F,有G[N(F)-V(F)]连通,则称G是H-局部连通的。本文证明:阶数≥8的连通、P3-局部连通的[5,3]-图是1-2可扩的(这里P3表示3阶路)。

A graph G is a E s, tl-graph if there are at least t edges in every included subgraph of s vertices. Let H be a graph. A graph G is H-locally connected if G[ N（F） - V（F） ] is connected for its any subgraph F isomorphic to H. This paper proves that a connected and P3-1ocally connected [ 5,3 ]-graph, whose order n ≥ 8 , is ]-2 extendable, （ P3 is an order 3 path. ）