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Abstract：
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(wg)(D) and the weak game colouring number wgcol(D) of digraphs D. It is proved that if D is an oriented planar graph, then chi(wg)(D) ＜= wgcol(D) ＜= 9, and if D is an oriented outerplanar graph, then chi(wg)(D) ＜= wgcol(D) ＜= 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) ＜= 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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ELECTRONIC JOURNAL OF COMBINATORICS
ISSN： 1077-8926
Year： 2010
Issue： 1
Volume： 17
0 . 6 2 6
JCR@2010
0 . 7 0 0
JCR@2023
ESI Discipline： MATHEMATICS;
JCR Journal Grade：2
CAS Journal Grade：3
Cited Count：
WoS CC Cited Count： 6
SCOPUS Cited Count：
ESI Highly Cited Papers on the List： 0 Unfold All
WanFang Cited Count：
Chinese Cited Count：
30 Days PV： 5
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