Strong oriented chromatic number of planar graphs without cycles of specific lengths

A strong oriented k-coloring of an oriented graph G is a homomorphism from G to H having k vertices labelled by the k elements of an abelian additive group M, such that for any pairs of arcs -uv and zt of G, we have (v)-(u) = -((t)-(z)). The strong oriented chromatic number s(G) is the smallest k such that G admits a strong oriented k-coloring. In this paper, we consider the following problem: Let i 4 be an integer. Let G be an oriented planar graph without cycles of lengths 4 to i. What is the strong oriented chromatic number of G?

• Type: Journal
• Year: 2008
• Where: ENDM
• Authors: Mickaël Montassier, Pascal Ochem, Alexandre Pinlou
• Keywords: ENDM 2008, Oriented Chromatic Number, Oriented Graph, Strong Oriented K-coloring