Chromatic number and Hamiltonicity of graphs

Abstract

Let $G$ be a $k$-connected ($k>2$) graph of order $n$. If $\chi (G)>n-k$, then $G$ is Hamiltonian or $K_k\vee (K_{n-2k})$ with $n>2k+1$, where $\chi (G)$ is the chromatic number of the graph $G$.