Improved bounds for coloring locally sparse hypergraphs

Abstract

We show that, for every $k\ge 2$, every $k$-uniform hypergaph of degree $\hat{I}”$ and girth at least $5$ is efficiently $(1+o(1))(k-1)(\hat{I}”/\ln \hat{I}”{)}^{1/(k-1)}$-list colorable. As an application (and to the best of our knowledge) we obtain the currently best algorithm for list-coloring random hypergraphs of bounded average degree.