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Journal Articles Discrete Mathematics Year : 2009

An Oriented Coloring of Planar Graphs with Girth at Least Five

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].

Dates and versions

lirmm-00371599 , version 1 (30-03-2009)

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