{"docId":418,"paperId":418,"url":"https:\/\/dmtcs.episciences.org\/418","doi":"10.46298\/dmtcs.418","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":83,"name":"Vol. 10 no. 1"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"lirmm-00184811","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/lirmm-00184811v1","dateSubmitted":"2015-03-26 16:19:48","dateAccepted":"2015-06-09 14:46:46","datePublished":"2008-01-10 08:00:00","titles":{"en":"Strong Oriented Chromatic Number of Planar Graphs without Short Cycles"},"authors":["Montassier, Mickael","Ochem, Pascal","Pinlou, Alexandre"],"abstracts":{"en":"Let M be an additive abelian group. An M-strong-oriented coloring of an oriented graph G is a mapping f from V(G) to M such that f(u) <> j(v) whenever uv is an arc in G and f(v)\u2212f(u) <> \u2212(f(t)\u2212f(z)) whenever uv and zt are two arcs in G. The strong oriented chromatic number of an oriented graph is the minimal order of a group M such that G has an M-strong-oriented coloring. This notion was introduced by Nesetril and Raspaud [Ann. Inst. Fourier, 49(3):1037-1056, 1999]. We prove that the strong oriented chromatic number of oriented planar graphs without cycles of lengths 4 to 12 (resp. 4 or 6) is at most 7 (resp. 19). Moreover, for all i \u2265 4, we construct outerplanar graphs without cycles of lengths 4 to i whose oriented chromatic number is 7."},"keywords":[["Graphs"],["Algorithms"],"[INFO.INFO-DM] Computer Science [cs]\/Discrete Mathematics [cs.DM]"]}