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The relaxed game chromatic number of outerplanar graphs

✍ Scribed by Charles Dunn; Hal A. Kierstead

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 92 KB
Volume: 46
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10172

No coin nor oath required. For personal study only.

✦ Synopsis

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. © 2004 Wiley Periodicals, Inc. J Graph Theory 46:69–78, 2004

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