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Mixed graph colorings

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  • Pierre Hansen
  • Julio Kuplinsky
  • Dominique Werra

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 γ π (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. Copyright Physica-Verlag 1997

Suggested Citation

  • Pierre Hansen & Julio Kuplinsky & Dominique Werra, 1997. "Mixed graph colorings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 145-160, February.
    • Handle: RePEc:spr:mathme:v:45:y:1997:i:1:p:145-160
    DOI: 10.1007/BF01194253
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    References listed on IDEAS

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    1. Egon Balas, 1969. "Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm," Operations Research, INFORMS, vol. 17(6), pages 941-957, December.
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    Cited by:

    1. Ahmed Kouider & Hacène Ait Haddadène & Samia Ourari & Ammar Oulamara, 2017. "Mixed graph colouring for unit-time scheduling," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1720-1729, March.
    2. Peter Damaschke, 2019. "Parameterized Mixed Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 362-374, August.
    3. Yuri N. Sotskov, 2020. "Mixed Graph Colorings: A Historical Review," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    4. Rupkumar Mahapatra & Sovan Samanta & Madhumangal Pal & Tofigh Allahviranloo & Antonios Kalampakas, 2024. "A Study on Linguistic Z-Graph and Its Application in Social Networks," Mathematics, MDPI, vol. 12(18), pages 1-24, September.
    5. Hua Nam Son, 2016. "On the modelling of structured organizations," Logisztika - Informatika - Menedzsment, Budapest Business School, vol. 2016(1), pages 59-69.

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