Graphs and Combinatorics

, Volume 32, Issue 3, pp 851–859 | Cite as

Free Choosability of Outerplanar Graphs

Original Paper

Abstract

A graph G is free (ab)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex \(u\ne v\), the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition for a cycle to be free (ab)-choosable is given. As a corollary, we obtain almost optimal results about the free (ab)-choosability of outerplanar graphs.

Keywords

Coloring Choosability Free choosability Cycle Outerplanar graph 

Mathematics Subject Classification

05C15 05C38 05C10 

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Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Institut de Mathématiques de ToulonUniversité de ToulonLa GardeFrance
  2. 2.Institut de Mathématiques de MarseilleMarseilleFrance
  3. 3.LE2I UMR 6306, CNRS, Arts et MétiersUniversité Bourgogne Franche-ComtéDIJONFrance

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