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Keywords:

  • equitable coloring;
  • list coloring;
  • choosable;
  • maximum degree

Abstract

A graph G is equitably k-choosable if for every k-list assignment L there exists an L-coloring of G such that every color class has at most inline image vertices. We prove results toward the conjecture that every graph with maximum degree at most r is equitably inline image-choosable. In particular, we confirm the conjecture for inline image and show that every graph with maximum degree at most r and at least r3 vertices is equitably inline image-choosable. Our proofs yield polynomial algorithms for corresponding equitable list colorings.