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List colorings of -partite -graphs
A -uniform hypergraph (or -graph) is -partite if
can be partitioned into sets such that each edge in
contains precisely one vertex from each . In this note, we consider list
colorings for such hypergraphs. We show that for any if each
vertex is assigned a list of size , then admits a
proper -coloring, provided is sufficiently large. Up to a constant
factor, this matches the bound on the chromatic number of simple -graphs
shown by Frieze and Mubayi, and that on the list chromatic number of triangle
free -graphs shown by Li and Postle. Our results hold in the more general
setting of "color-degree" as has been considered for graphs. Furthermore, we
establish a number of asymmetric statements matching results of Alon, Cambie,
and Kang for bipartite graphs.Comment: 12 page