Longest Cycles in 2-Connected Quasi-Claw-Free Graphs

摘要

A graph G is called quasi-claw-free if it satisfies the property:d（x,y）=2 there exists a vertex u∈N（x）∩N（y）such that N[u]■N[x]∪N[y].In this paper,we show that every 2-connected quasi-claw-free graph of order n with G■F contains a cycle of length at least min{3δ+2,n},where F is a family of graphs.