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arXiv · 2507.05548

Total coloring graphs with large minimum degree

Owen Henderschedt·Jessica McDonald·Songling Shan
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Abstract

We prove that for all $\varepsilon>0$, there exists a positive integer $n_0$ such that if $G$ is a graph on $n\geq n_0$ vertices with $δ(G)\geq\tfrac{1}{2}(1 + \varepsilon)n$, then $G$ satisfies the Total Coloring Conjecture, that is, $χ_T(G)\leq Δ(G)+2$.

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Owen Henderschedt, Jessica McDonald, Songling Shan. 2025-07-08. Total coloring graphs with large minimum degree. https://arxiv.org/abs/2507.05548

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