## Abstract We introduce the (__a,b__)βcoloring game, an asymmetric version of the coloring game played by two players Alice and Bob on a finite graph, which differs from the standard version in that, in each turn, Alice colors __a__ vertices and Bob colors __b__ vertices. We also introduce a relat
Directed defective asymmetric graph coloring games
β Scribed by Stephan Dominique Andres
- Book ID
- 108112825
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 603 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0166-218X
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## Abstract This article proves the following result: Let __G__ and __G__β² be graphs of orders __n__ and __n__β², respectively. Let __G__^\*^ be obtained from __G__ by adding to each vertex a set of __n__β² degree 1 neighbors. If __G__^\*^ has game coloring number __m__ and __G__β² has acyclic chromat
This paper discusses a variation of the game chromatic number of a graph: the game coloring number. This parameter provides an upper bound for the game chromatic number of a graph. We show that the game coloring number of a planar graph is at most 19. This implies that the game chromatic number of a