On list chromatic numbers of 2-colorable hypergraphs

TL;DR

This paper establishes bounds on the list chromatic number of 2-colorable hypergraphs, extending previous results and providing exact values for certain regular hypergraphs, with implications for sparse hypergraph coloring.

Contribution

It generalizes existing bounds on list chromatic numbers for 2-colorable hypergraphs and determines exact values for regular hypergraphs.

Findings

A $k$-uniform $k$-regular hypergraph has list chromatic number 2 for $k geq 4$.

Provides bounds on the list chromatic number of complete 2-colorable hypergraphs.

Extends bounds of Schauz and relates to Erd{"H}os--Rubin--Taylor theorem.

Abstract

We give an upper bound on the list chromatic number of a 2-colorable hypergraph which generalizes the bound of Schauz on $k$-partite $k$-uniform hypergraphs. It makes sense for sparse hypergraphs: in particular we show that a $k$-uniform $k$-regular hypergraph has the list chromatic number 2 for $k \geq 4$. Also we obtain both lower and upper bound on the list chromatic number of a complete $s$-uniform 2-colorable hypergraph in the vein of Erd{\H o}s--Rubin--Taylor theorem.