Equitable List Coloring of Graphs with Bounded Degree

Authors


  • Contract grant sponsor: NSA; Contract grant number: MDA 904-03-1-0007; Contract grant sponsor: NSF; Contract grant number: DMS-0901520 (H. A. K.); Contract grant sponsor: NSF; Contract grant number: DMS-0965587; Contract grant sponsor: Russian Foundation for Basic Research; Contract grant number: 09-01-00244-a (A. V. K.).

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 math formula vertices. We prove results toward the conjecture that every graph with maximum degree at most r is equitably math formula-choosable. In particular, we confirm the conjecture for math formula and show that every graph with maximum degree at most r and at least r3 vertices is equitably math formula-choosable. Our proofs yield polynomial algorithms for corresponding equitable list colorings.

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