Consider the following two-person game on a graph G . Players I and II move alternatively to color a yet uncolored vertex of G properly using a pre-specified set of colors . Furthermore , Player II can only use the colors that have been used , unless he is forced to use a new color to guarantee that
The incidence game chromatic number
β Scribed by Stephan Dominique Andres
- Book ID
- 108112724
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 535 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
This note proves that the game chromatic number of an outerplanar graph is at most 7. This improves the previous known upper bound of the game chromatic number of outerplanar graphs.
## Abstract The (__r__,__d__)βrelaxed 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 Ξ± is legal for an uncolored vertex __u__ if __u__ is adjacent to at most __d__ vert
We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particula