On 2-factors in 5-cycle connected claw-free graphs

Abstract

A cycle of length i is called an i-cycle. A graph G is 5-cycle connected if for every pair of edges ei and e2 in E(G), G has a sequence of l-cycles (3 ≤ I ≤ 5) C1 C2..., Cr such that ei ϵ E(C1) and e2 ϵ E(C2) and E(Ci) ∩ E{Ci+1) ≠ θ for i = 1,2, ... ,r - 1. In this paper, we show that every 5-cycle connected claw-free graph has a 2-factor. This result is best possible.