A Note on Hamiltonian Cycles in $K_{1,r}$ – Free Graphs

Abstract

A graph is called $K_{1,r}$-free if it does not contain $K_{1,r}$ as an induced subgraph. In this paper we generalize a theorem of Markus for Hamiltonicity of $2$-connected $K_{1,r}$-free ($r\ge 5$) graphs and present a sufficient condition for $1$-tough $K_{1,r}$-free ($r\ge 4$) graphs to be Hamiltonian.