## 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
The 6-relaxed game chromatic number of outerplanar graphs
β Scribed by Jiaojiao Wu; Xuding Zhu
- Book ID
- 108113955
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 447 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
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 A proper edge coloring of a graph __G__ is called acyclic if there is no 2βcolored cycle in __G__. The acyclic edge chromatic number of __G__, denoted by Ο(__G__), is the least number of colors in an acyclic edge coloring of __G__. In this paper, we determine completely the acyclic edge
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