Oriented Coloring of Triangle-Free Planar Graphs and 2-Outerplanar Graphs

Pascal Ochem 1 Alexandre Pinlou 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A graph is planar if it can be embedded on the plane without edge-crossings. A graph is 2-outerplanar if it has a planar embedding such that the subgraph obtained by removing the vertices of the external face is outerplanar (i.e. with all its vertices on the external face). An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented triangle-free planar graph has an oriented chromatic number at most 40, that improves the previous known bound of 47 [Borodin, O. V. and Ivanova, A. O., An oriented colouring of planar graphs with girth at least 4, Sib. Electron. Math. Reports, vol. 2, 239-249, 2005]. We also prove that every oriented 2-outerplanar graph has an oriented chromatic number at most 40, that improves the previous known bound of 67 [Esperet, L. and Ochem, P. Oriented colouring of 2-outerplanar graphs, Inform. Process. Lett., vol. 101(5), 215-219, 2005].
Type de document :
Article dans une revue
Graphs and Combinatorics, Springer Verlag, 2014, 30 (2), pp.439-453. 〈10.1007/s00373-013-1283-2〉
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00780910
Contributeur : Alexandre Pinlou <>
Soumis le : vendredi 25 janvier 2013 - 09:00:46
Dernière modification le : jeudi 24 mai 2018 - 15:59:22

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Pascal Ochem, Alexandre Pinlou. Oriented Coloring of Triangle-Free Planar Graphs and 2-Outerplanar Graphs. Graphs and Combinatorics, Springer Verlag, 2014, 30 (2), pp.439-453. 〈10.1007/s00373-013-1283-2〉. 〈lirmm-00780910〉

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