On the oriented chromatic number of grids

  • Authors:

  • Guillaume Fertin;André Raspaud;Arup Roychowdhury

  • Affiliations:

  • IRIN UPRES-EA 2157, Université de Nantes, 2 rue de la Houssinière, BP 92208, F44322 Nantes Cedex 3, France;LaBRI U.M.R. 5800, Université Bordeaux I, 351 Cours de la Libération, F33405 Talence Cedex, France;Oracle India Private Limited, Hi-Tec City, Madhapur, Hyderabad 500081, India

  • Venue:
  • Information Processing Letters
  • Year:
  • 2003

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Abstract

n 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)∈ A(G) are assigned colors c(u) and c(v), then for any (z, t) ∈ 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.