scholarly journals On the Oriented Game Chromatic Number

10.37236/1613 ◽  
2000 ◽  
Vol 8 (2) ◽  
Author(s):  
J. Nešetřil ◽  
E. Sopena
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graph ◽  
Game Chromatic Number ◽  
Oriented Path

We consider the oriented version of a coloring game introduced by Bodlaender [On the complexity of some coloring games, Internat. J. Found. Comput. Sci. 2 (1991), 133–147]. We prove that every oriented path has oriented game chromatic number at most 7 (and this bound is tight), that every oriented tree has oriented game chromatic number at most 19 and that there exists a constant $t$ such that every oriented outerplanar graph has oriented game chromatic number at most $t$.

scholarly journals Game Colouring Directed Graphs

10.37236/283 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Daqing Yang ◽  
Xuding Zhu
Keyword(s):  
Planar Graph ◽  
Chromatic Number ◽  
Lower Bounds ◽  
Directed Graphs ◽  
Upper And Lower Bounds ◽  
Outerplanar Graph ◽  
Game Chromatic Number

In this paper, a colouring game and two versions of marking games (the weak and the strong) on digraphs are studied. We introduce the weak game chromatic number $\chi_{\rm wg}(D)$ and the weak game colouring number ${\rm wgcol}(D)$ of digraphs $D$. It is proved that if $D$ is an oriented planar graph, then $\chi_{\rm wg}(D)$ $\le {\rm wgcol}(D) \le 9$, and if $D$ is an oriented outerplanar graph, then $\chi_{\rm wg}(D)$ $\le {\rm wgcol}(D) \le 4$. Then we study the strong game colouring number ${\rm sgcol}\left( D \right)$ (which was first introduced by Andres as game colouring number) of digraphs $D$. It is proved that if $D$ is an oriented planar graph, then ${\rm sgcol}\left( D \right) \le 16$. The asymmetric versions of the colouring and marking games of digraphs are also studied. Upper and lower bounds of related parameters for various classes of digraphs are obtained.

scholarly journals Relaxed game chromatic number of trees and outerplanar graphs

2004 ◽  
Vol 281 (1-3) ◽  
pp. 209-219 ◽  
Author(s):  
Wenjie He ◽  
Jiaojiao Wu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number

On the game chromatic number of splitting graphs of path and cycle

2019 ◽  
Vol 795 ◽  
pp. 50-56 ◽  
Author(s):  
Muhammad S. Akhtar ◽  
Usman Ali ◽  
Ghulam Abbas ◽  
Mutahira Batool
Keyword(s):  
Chromatic Number ◽  
Game Chromatic Number

scholarly journals The game chromatic number of random graphs

2008 ◽  
Vol 32 (2) ◽  
pp. 223-235 ◽  
Author(s):  
Tom Bohman ◽  
Alan Frieze ◽  
Benny Sudakov
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
Game Chromatic Number

scholarly journals Game Chromatic Number of Some Regular Graphs

2019 ◽  
Vol 09 (04) ◽  
pp. 159-164 ◽  
Author(s):  
Ramy Shaheen ◽  
Ziad Kanaya ◽  
Khaled Alshehada
Keyword(s):  
Chromatic Number ◽  
Regular Graphs ◽  
Game Chromatic Number
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