# On the oriented chromatic number of grids

Abstract : In this paper, we focus on the oriented coloring of graphs. Oriented coloring is a coloring of the vertices of an oriented graph $G$ without symmetric arcs such that (i) no two neighbors in $G$ are assigned the same color, and (ii) if two vertices $u$ and $v$ such that $(u,v)\in A(G)$ are assigned colors $c(u)$ and $c(v)$, then for any $(z,t)\in A(G)$, we cannot have simultaneously $c(z)=c(v)$ and $c(t)=c(u)$. The oriented chromatic number of an unoriented graph $G$ is the smallest number $k$ of colors for which any of the orientations of $G$ can be colored with $k$ colors. The main results we obtain in this paper are bounds on the oriented chromatic number of particular families of planar graphs, namely 2-dimensional grids, fat trees and fat fat trees.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00307790
Contributor : Guillaume Fertin <>
Submitted on : Tuesday, September 15, 2009 - 10:18:33 AM
Last modification on : Thursday, April 5, 2018 - 10:36:48 AM
Document(s) archivé(s) le : Saturday, November 26, 2016 - 1:23:33 AM

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Oriented_IPL.pdf
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### Identifiers

• HAL Id : hal-00307790, version 1
• ARXIV : 0909.2608

### Citation

Guillaume Fertin, André Raspaud, Arup Roychowdhury. On the oriented chromatic number of grids. Information Processing Letters, Elsevier, 2003, 85 (5), pp.261-266. ⟨hal-00307790⟩

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