Chromatic Number and Hamiltonicity of Graphs

Abstract

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