Hamiltonicity of edge-chromatic critical graphs

Given a graph $G$, denote by $\mathrm{\Delta }$ and ${\chi }^{\mathrm{\prime }}$ the maximum degree and the chromatic index of $G$, respectively. A simple graph $G$ is called {\it edge-$\mathrm{\Delta }$-critical} if ${\chi }^{\mathrm{\prime }}(G)=\mathrm{\Delta }+1$ and ${\chi }^{\mathrm{\prime }}(H)\le \mathrm{\Delta }$ 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.