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Article Dans Une Revue European Journal of Combinatorics Année : 2009

Convex circuit-free coloration of an oriented graph

Résumé

We introduce the Convex Circuit-Free coloration and Convex Circuit-Free chromatic numberView the MathML source of an oriented graph View the MathML source and establish various basic results. We show that the problem of deciding if an oriented graph verifies View the MathML source is NP-complete if k≥3, and polynomial if k≤2. We introduce an algorithm which finds the optimal convex circuit-free coloration for tournaments, and characterize the tournaments that are vertex-critical for the convex circuit-free coloration.

Dates et versions

hal-00716574 , version 1 (10-07-2012)

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Jean-François Culus, Bertrand Jouve. Convex circuit-free coloration of an oriented graph. European Journal of Combinatorics, 2009, 30 (1), pp.43-52. ⟨10.1016/j.ejc.2008.02.012⟩. ⟨hal-00716574⟩
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