  We show that the chromatic index of a hypergraph $\mathcal{H}$ satisfies
Berge-F\"uredi conjectured bound $\mathrm{q}(\mathcal{H})\le
\Delta([\mathcal{H}]_2)+1$ 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.
