About Berge-Füredi's conjecture on the chromatic index of hypergraphs
Résumé
We show that the chromatic index of a hypergraph $\mathcal{H}$ satisfies {Berge-F\"uredi} conjectured bound $q(\mathcal{h})\le \Delta([\mathcal{H}]_2)+1$ 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 {Erd\H{o}s-Faber-Lov\'asz} Conjecture which deals with the coloring of a family of cliques that intersect pairwise in at most one vertex.
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