About Berge–Füredi’s conjecture on the chromatic index of hypergraphs - Bretto, Alain; Faisant, Alain; Hennecart, François (Comptes Rendus. Mathématique, 2025)
We prove that the chromatic index of a hypergraph $\mathcal{H}$ satisfies the Berge–Füredi conjectured bound $\mathrm{q}(\mathcal{H}\le \Delta \bigl ([\mathcal{H}_2]\bigr )+1$ under certain hypotheses on the antirank $\mathrm{ar}(\mathcal{H})$ or on the maximum degree $\Delta (\mathcal{H})$. This provides sharp information in connection with the Erdős–Faber–Lovász conjecture which deals with the coloring of a family of cliques that intersect pairwise in at most one vertex.