2023/11/06 by Dhawan, Abhishek · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.03111
A k-uniform hypergraph (or k-graph) H = (V, E) is k-partite if V can be partitioned into k sets V1, …, Vk such that each edge in E contains precisely one vertex from each Vi. In this note, we consider list colorings for such hypergraphs. We show that for any ε > 0 if each vertex v ∈ V(H) is assigned a list of size |L(v)| ≥ ((k-1+ε)Δ/log Δ)1/(k-1), then H admits a proper L-coloring, provided Δ is sufficiently large. Up to a constant factor, this matches the bound on the chromatic number of simple k-graphs shown by Frieze and Mubayi, and that on the list chromatic number of triangle free k-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.