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
β¦ LIBER β¦
The coloring of graphs in a linear number of steps
β Scribed by A. A. Kalnin'sh
- Publisher
- Springer US
- Year
- 1974
- Tongue
- English
- Weight
- 830 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1573-8337
No coin nor oath required. For personal study only.
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## Abstract The distance coloring number __X__~__d__~(__G__) of a graph __G__ is the minimum number __n__ such that every vertex of __G__ can be assigned a natural number __m__ β€ __n__ and no two vertices at distance __i__ are both assigned __i__. It is proved that for any natural number __n__ ther