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Keywords:

  • graph coloring;
  • equitable coloring;
  • outerplanar graph;
  • tree;
  • list coloring

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 equation image vertices. A graph is equitably k-choosable if such a coloring exists whenever the lists all have size k. We prove that G is equitably k-choosable when equation image unless G contains equation image or k is odd and equation image. For forests, the threshold improves to equation image. If G is a 2-degenerate graph (given k ≥ 5) or a connected interval graph (other than equation image), then G is equitably k-choosable when equation image. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 166–177, 2003