Competitive Colorings of Oriented Graphs

Ne set ril and Sopena introduced a concept of oriented game chromatic number and developed a general technique for bounding this parameter. In this paper, we combine their technique with concepts introduced by several authors in a series of papers on game chromatic number to show that for every positive integer k ,t here exists an integer t so that if C is a topologically closed class of graphs and C does not contain a complete graph on k vertices, then whenever G is an orientation of a graph from C, the oriented game chromatic number of G is at most t .I n particular, oriented planar graphs have bounded oriented game chromatic number. This answers a question raised by Ne set ril and Sopena. We also answer a second question raised by Ne set ril and Sopena by constructing a family of oriented graphs for which oriented game chromatic number is bounded but extended Go number is not.

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