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arXiv · 2403.09518

About Berge-Füredi's conjecture on the chromatic index of hypergraphs

Alain Bretto·Alain Faisant·François Hennecart
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Abstract

We show that the chromatic index of a hypergraph $\mathcal{H}$ satisfies Berge-Füredi conjectured bound $\mathrm{q}(\mathcal{H})\le Δ([\mathcal{H}]_2)+1$ under certain hypotheses on the antirank $\mathrm{ar}(\mathcal{H})$ or on the maximum degree $Δ(\mathcal{H})$. This provides sharp information in connection with Erdős-Faber-Lovász Conjecture which deals with the coloring of a family of cliques that intersect pairwise in at most one vertex.

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Alain Bretto, Alain Faisant, François Hennecart. 2024-03-14. About Berge-Füredi's conjecture on the chromatic index of hypergraphs. https://arxiv.org/abs/2403.09518

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