The adaptable choosability number grows with the choosability number

The adaptable choosability number of a multigraph G , denoted c h a ( 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 = u v has both u and v colored with the label of e . We show that c h a grows with c h , i.e. there is a function f tending to infinity such that c h a ( G ) ≥ f ( c h ( G ) ) .