The adaptable choosability number grows with the choosability number

Abstract

The adaptable choosability number of a multigraph G, denoted c ha(G), is the smallest integer k such that every edge labeling of G and assignment of lists of size k to the vertices of G permits a list coloring of G in which no edge e=uv has both u and v colored with the label of e. We show that c ha grows with ch, i.e. there is a function f tending to infinity such that c ha(G)