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<title lang=en>Convex circuit-free coloration of an oriented graph</title>
<creator>Culus, Jean-François</creator>
<creator>Jouve, Bertrand</creator>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Institut de Mathématiques de Toulouse UMR5219 (IMT) ; Centre National de la Recherche Scientifique (CNRS) - Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) - PRES Université de Toulouse - Université Paul Sabatier - Toulouse 3 (UPS) - Université Toulouse 2 (UT2) - Université Toulouse 1 Capitole (UT1)</contributor>
<description>International audience</description>
<source>ISSN: 0195-6698</source>
<source>EISSN: 1095-9971</source>
<source>European Journal of Combinatorics</source>
<publisher>Elsevier</publisher>
<identifier>hal-00716574</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00716574</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00716574</source>
<source>European Journal of Combinatorics, Elsevier, 2009, 30 (1), pp.43-52. 〈10.1016/j.ejc.2008.02.012〉</source>
<identifier>DOI : 10.1016/j.ejc.2008.02.012</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ejc.2008.02.012</relation>
<language>en</language>
<subject>[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>2009-01-01</date>
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