10.46298/dmtcs.418
https://dmtcs.episciences.org/418
Montassier, Mickael
Mickael
Montassier
Ochem, Pascal
Pascal
Ochem
Pinlou, Alexandre
Alexandre
Pinlou
Strong Oriented Chromatic Number of Planar Graphs without Short Cycles
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)−f(u) <> −(f(t)−f(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 ≥ 4, we construct outerplanar graphs without cycles of lengths 4 to i whose oriented chromatic number is 7.
episciences.org
Graphs
Algorithms
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
2015-06-09
2008-01-10
2008-01-10
en
journal article
https://hal.science/lirmm-00184811v1
1365-8050
https://dmtcs.episciences.org/418/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 10 no. 1
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