Hamiltonicity of edge-chromatic critical graphs

TL;DR

This paper proves that large enough edge-$ riangle$-critical graphs with high maximum degree are Hamiltonian, advancing understanding of Hamiltonicity conditions in edge-chromatic critical graphs.

Contribution

It establishes a new sufficient condition for Hamiltonicity in edge-chromatic critical graphs based on maximum degree and order.

Findings

Edge-$ riangle$-critical graphs with $ riangle ext{ at least } rac{2n}{3}+12$ are Hamiltonian.

Provides a degree-based criterion for Hamiltonicity in critical graphs.

Extends previous results on Hamiltonian properties of 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.