On the oriented chromatic number of graphs with given excess |
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Authors: | Mohammad Hosseini Dolama |
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Institution: | a Department of Mathematics, Urmia University, Urmia, Iran b LaBRI, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France |
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Abstract: | The excess of a graph G is defined as the minimum number of edges that must be deleted from G in order to get a forest. We prove that every graph with excess at most k has chromatic number at most and that this bound is tight. Moreover, we prove that the oriented chromatic number of any graph with excess k is at most k+3, except for graphs having excess 1 and containing a directed cycle on 5 vertices which have oriented chromatic number 5. This bound is tight for k?4. |
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Keywords: | Graph coloring Graph homomorphism Oriented graph coloring Betti number |
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