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Mixed graph colorings

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Abstract

A mixed graphG π contains both undirected edges and directed arcs. Ak-coloring ofG π 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 thatG π 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.

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References

  1. Atkinson MD, Sack J-R, Santoro N, Strothotte T (1986) Min-max heaps and generalized priority queues. Communications of the Association for Computing Machinery 29:996–1000

    Google Scholar 

  2. Balas E (1969) Machine sequencing via disjunctive graphs: An implicit enumeration approach. Operations Research 17:941–957

    Google Scholar 

  3. Gallai T (1968) On directed paths and circuits. In: Erdös P, Katona G (Eds.) Theory of graphs — proceedings of the colloquium held at Tihany, Hungary. Academic Press

    Google Scholar 

  4. Matula DW, Marble G, Isaacson JD (1972) Graph coloring algorithms. In: Read RC (Ed.) Graph Theory and Computing. Academic Press

  5. Roy B (1966) Prise en compte des contraintes disjonctives dans les méthodes de chemin critique. RAIRO 38:69–84

    Google Scholar 

  6. Roy B (1967) Nombre chromatique et plus longs chemins d'un graphe. Revue Française d'Informatique et de Recherche Opérationnelle 1:129–132

    Google Scholar 

  7. Tarjan RE (1983) Data structures and network algorithms. SIAM

  8. Vitaver LM (1962) Determination of minimal colorings for vertices of a graph by means of Boolean powers of the adjacency martix. Soviet Mathematics — Doklady 3, no 6:1687–1688

    Google Scholar 

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Authors and Affiliations

  1. Ecole des Hautes Etudes Commerciales, GERAD, Montréal, Québec, Canada

    Pierre Hansen

  2. 6, Washington Drive, 07446, Ramsey, NJ, USA

    Julio Kuplinsky

  3. Départment de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Chaire de Recherche Operationelle, 1015, Lausanne, Switzerland

    Dominique de Werra

Authors
  1. Pierre Hansen
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  2. Julio Kuplinsky
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  3. Dominique de Werra
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Hansen, P., Kuplinsky, J. & de Werra, D. Mixed graph colorings. Mathematical Methods of Operations Research 45, 145–160 (1997). https://doi.org/10.1007/BF01194253

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  • DOI: https://doi.org/10.1007/BF01194253

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