Game Colouring Directed Graphs
نویسندگان
چکیده
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 χwg(D) and the weak game colouring number wgcol(D) of digraphs D. It is proved that if D is an oriented planar graph, then χwg(D) 6 wgcol(D) 6 9, and if D is an oriented outerplanar graph, then χwg(D) 6 wgcol(D) 6 4. Then we study the strong game colouring number sgcol (D) (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 sgcol (D) 6 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.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010