Hamiltonicity of edge-chromatic critical graphs

Abstract

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.

arXiv admin note: text overlap with arXiv:1708.01279