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arXiv · 2309.10876

On Vizing's problem for triangle-free graphs

Ross J. Kang·Matthieu Rosenfeld
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Abstract

We prove that $χ(G) \le \lceil (Δ+1)/2\rceil+1$ for any triangle-free graph $G$ of maximum degree $Δ$ provided $Δ\ge 524$. This gives tangible progress towards an old problem of Vizing, in a form cast by Reed. We use a method of Hurley and Pirot, which in turn relies on a new counting argument of the second author.

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Ross J. Kang, Matthieu Rosenfeld. 2025-09-04. On Vizing's problem for triangle-free graphs. https://arxiv.org/abs/2309.10876

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