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
Orderings on Graphs and Game Coloring Number
β Scribed by H. A. Kierstead; Daqing Yang
- Book ID
- 111603067
- Publisher
- Springer Netherlands
- Year
- 2003
- Tongue
- English
- Weight
- 107 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0167-8094
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a planar graph and let g(G) and Γ(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (i) -cycles (though it may contain 3-cycles). These results are applied to find the following upper bounds for the game coloring n
## 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