Hamiltonicity of edge chromatic critical graphs

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

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