Hamiltonicity of edge-chromatic critical graphs

Abstract

Given a graph $G$, denote by $Δ$ and $χ^\prime$ the maximum degree and the chromatic index of $G$, respectively. A simple graph $G$ is called {\it edge-$Δ$-critical} if $χ^\prime(G)=Δ+1$ and $χ^\prime(H)\leΔ$ for every proper subgraph $H$ of $G$. We proved that every edge chromatic critical graph of order $n$ with maximum degree at least $\frac{2n}{3}+12$ is Hamiltonian.