The Matching Number and Hamiltonicity of Quasi-Claw-Free Graphs

Abstract

A graph $G$ is quasi-claw-free if it satisfies the property: $d(x,y)=2$ implies there exists $u\in N(x)\cap N(y)$ such that $N[u]\subseteq N[x]\cup N[y]$. The matching number of a graph $G$ is the size of a maximum matching in the graph. In this note, we present a sufficient condition involving the matching number for the Hamiltonicity of quasi-claw-free graphs.