Analogues of cliques for oriented coloring

• Autorzy: William F. Klostermeyer , Gary MacGillivray
• Języki publikacji: EN

Abstrakty

EN

We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of vertices in D are joined by a directed path of length at most two.

Słowa kluczowe

EN

graph coloring; oriented coloring; clique; planar graph

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C20: Directed graphs (digraphs), tournaments
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 3
• Strony: 373-387

Daty

wydano

2004

otrzymano

2002-10-15

poprawiono

2004-03-11

Twórcy

autor

William F. Klostermeyer

• Department of Computer and Information Sciences, University of North Florida, Jacksonville, FL 32224-2669, U.S.A.

autor

Gary MacGillivray

• Department of Mathematics and Statistics, University of Victoria, Victoria, Canada

Bibliografia

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• [7] E. Sopena, Oriented graph coloring, Discrete Math. 229 (2001) 359-369, doi: 10.1016/S0012-365X(00)00216-8.
• [8] E. Sopena, There exist oriented planar graphs with oriented chromatic number at least sixteen, Info. Proc. Letters 81 (2002) 309-312, doi: 10.1016/S0020-0190(01)00246-0.
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Identyfikatory

DOI

10.7151/dmgt.1237