A dualistic approach to bounding the chromatic number of a graph

Authors:
Jaroslav Nešetřil;Claude Tardif
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské nám.25, 11800 Praha 1, Czech Republic;Department of Mathematics and Statistics, University of Regina, Regina SK, S4S 0A2, Canada
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

We give a new and more direct proof of the characterization theorem for finitary homomorphism dualities of directed graphs. This result may be viewed as a characterization of Gallai-Hasse-Roy-Vitaver type theorems. We exhibit infinitely many examples where this general setting improves the bounds for chromatic number of graphs and we relate this to extremal problems for oriented graphs.