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

We show that the chromatic index of a hypergraph $\mathcal{H}$ satisfies Berge-Füredi conjectured bound $\mathrm{q}(\mathcal{H})\le \mathrm{\Delta }([\mathcal{H}{]}_2)+1$ under certain hypotheses on the antirank $\mathrm{a}\mathrm{r}(\mathcal{H})$ or on the maximum degree $\mathrm{\Delta }(\mathcal{H})$. 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.