Competitive colorings of oriented graphs

Henry Kierstead, W. T. Trotter

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Nešetřil 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, there 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. In particular, oriented planar graphs have bounded oriented game chromatic number. This answers a question raised by Nešetřil and Sopena. We also answer a second question raised by Nešetřil and Sopena by constructing a family of oriented graphs for which oriented game chromatic number is bounded but extended Go number is not.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalElectronic Journal of Combinatorics
Volume8
Issue number2 R
StatePublished - Dec 1 2001

Keywords

  • Chromatic number
  • Competitive algorithm
  • Oriented graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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