The Relaxed Game Chromatic Number of Outerplanar Graphs

Charles Dunn, Henry Kierstead

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

The (r,d)-relaxed coloring game is played by two players, Alice and Bob, on a graph G with a set of r colors. The players take turns coloring uncolored vertices with legal colors. A color α is legal for an uncolored vertex u if u is adjacent to at most d vertices that have already been colored with α, and every neighbor of u that has already been colored with α is adjacent to at most d - 1 vertices that have already been colored with α. Alice wins the game if eventually all the vertices are legally colored; otherwise, Bob wins the game when there comes a time when there is no legal move left. We show that if G is outerplanar then Alice can win the (2,8)-relaxed coloring game on G. It is known that there exists an outerplanar graph G such that Bob can win the (2,4)-relaxed coloring game on G.

Original languageEnglish (US)
Pages (from-to)69-78
Number of pages10
JournalJournal of Graph Theory
Volume46
Issue number1
DOIs
StatePublished - May 2004

Keywords

  • Competitive coloring
  • Outerplanar graph
  • Relaxed coloring

ASJC Scopus subject areas

  • Geometry and Topology

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