Equitable list‐coloring for graphs of maximum degree 3

Abstract

Abstract Given lists of available colors assigned to the vertices of a graph G , a list coloring is a proper coloring of G such that the color on each vertex is chosen from its list. If the lists all have size k , then a list coloring is equitable if each color appears on at most ⌈| V ( G )|/ k ⌉ vertices. A graph is equitably k ‐choosable if such a coloring exists whenever the lists all have size k . Kostochka, Pelsmajer, and West introduced this notion and conjectured that G is equitably k ‐choosable for k > Δ ( G ). We prove this for Δ( G ) = 3. We also show that every graph G is equitably k ‐choosable for k ≥ Δ( G )(Δ( G )−1)/2 + 2. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 1–8, 2004