## 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
Marking Games and the Oriented Game Chromatic Number of Partialk-Trees
β Scribed by H.A. Kierstead; Zs. Tuza
- Publisher
- Springer Japan
- Year
- 2003
- Tongue
- English
- Weight
- 118 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with
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Lu, Z., The harmonious chromatic number of a complete binary and trinary tree, Discrete Mathematics 118 (1993) 1655172.