Adapted List Coloring of Graphs and Hypergraphs

Abstract

We introduce and study adapted list coloring of graphs and hypergraphs. This is a generalization of ordinary list coloring and adapted coloring, and has more applications than these. We prove that the upper bounds on the adaptable choosability of graphs and uniform hypergraphs in terms of maximum degree are sufficiently stronger than those on the ordinary choosability, while the bounds in terms of degeneracy are the same. We also characterize simple graphs with adaptable choosability $2$.