Mathematical Methods of Operations Research

, Volume 45, Issue 1, pp 145–160

Mixed graph colorings

  • Pierre Hansen
  • Julio Kuplinsky
  • Dominique de Werra

DOI: 10.1007/BF01194253

Cite this article as:
Hansen, P., Kuplinsky, J. & de Werra, D. Mathematical Methods of Operations Research (1997) 45: 145. doi:10.1007/BF01194253


A mixed graphGπ contains both undirected edges and directed arcs. Ak-coloring ofGπ is an assignment to its vertices of integers not exceedingk (also called colors) so that the endvertices of an edge have different colors and the tail of any arc has a smaller color than its head. The chromatic number γπ(G) of a mixed graph is the smallestk such thatGπ admits ak-coloring. To the best of our knowledge it is studied here for the first time. We present bounds of γ(G), discuss algorithms to find this quantity for trees and general graphs, and report computational experience.

Key words

Graph coloring oriented graphs chromatic scheduling 

Copyright information

© Physica-Verlag 1997

Authors and Affiliations

  • Pierre Hansen
    • 1
  • Julio Kuplinsky
    • 2
  • Dominique de Werra
    • 3
  1. 1.Ecole des Hautes Etudes Commerciales, GERADMontréalCanada
  2. 2.RamseyUSA
  3. 3.Départment de MathématiquesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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