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An Oriented Coloring of Planar Graphs with Girth at Least Five

Alexandre Pinlou 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : 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 graph with a maximum average degree less than 10/3 and girth at least 5 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least 5 has an oriented chromatic number at most 16, that improves the previous known bound of 19 due to Borodin et al. [O.V. Borodin, A.V. Kostochka, J. Nešetřil, A. Raspaud, É. Sopena, On the maximum average degree and the oriented chromatic number of a graph, Discrete Math. 206 (1999) 77-89].
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00371599
Contributor : Alexandre Pinlou <>
Submitted on : Monday, March 30, 2009 - 7:49:52 AM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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Alexandre Pinlou. An Oriented Coloring of Planar Graphs with Girth at Least Five. Discrete Mathematics, Elsevier, 2009, 309, pp.2108-2118. ⟨10.1016/j.disc.2008.04.030⟩. ⟨lirmm-00371599⟩

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