Speaker: Nhi Dinh (UIUC)
Title: Choosability of multipartite hypergraphs
Abstract: A $k$-uniform hypergraph (or $k$-graph) $H = (V, E)$ is $k$-partite if $V$ can be partitioned into $k$ sets $V_1, \ldots, V_k$ such that each edge in $E$ contains precisely one vertex from each $V_i$. We show that $k$-partite hypergraphs of maximum degree $\Delta$ are $q$-choosable for any $q \geq \left(\frac{4}{5}(k-1 + o(1))\Delta/\log \Delta\right)^{1/(k-1)}$, moving past the shattering threshold in colorings of random hypergraphs.
Joint work with Peter Bradshaw, Abhishek Dhawan, Shlok Mulye, and Rohan Rathi.