Hamiltonian Paths in Connected Claw-Free Graphs

Abstract

Let $G$ be a connected claw-free graph of order $n$. If $G\notin M$ and the minimum degree of $G$ is at least $\frac{n}{4}$, then $G$ is traceable.Here, $M$ is a set of graphs such that each element in $M$ can be decomposed into three disjoint subgraphs $G_1$, $G_2$, $G_3$ and $E_G(G_i,G_j)=u_i{u}_j$, here $1\le i,j\le 3$ and $u_i\in G_i$, $1\le i\le 3$.