IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v45y1997i1p145-160.html
   My bibliography  Save this article

Mixed graph colorings

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF01194253
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF01194253?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Egon Balas, 1969. "Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm," Operations Research, INFORMS, vol. 17(6), pages 941-957, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peter Damaschke, 2019. "Parameterized Mixed Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 362-374, August.
    2. Yuri N. Sotskov, 2020. "Mixed Graph Colorings: A Historical Review," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    3. 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.
    4. Hua Nam Son, 2016. "On the modelling of structured organizations," Logisztika - Informatika - Menedzsment, Budapest Business School, vol. 2016(1), pages 59-69.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrea D'Ariano & Francesco Corman & Dario Pacciarelli & Marco Pranzo, 2008. "Reordering and Local Rerouting Strategies to Manage Train Traffic in Real Time," Transportation Science, INFORMS, vol. 42(4), pages 405-419, November.
    2. Steinhofel, K. & Albrecht, A. & Wong, C. K., 1999. "Two simulated annealing-based heuristics for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 118(3), pages 524-548, November.
    3. Selcuk Goren & Ihsan Sabuncuoglu & Utku Koc, 2012. "Optimization of schedule stability and efficiency under processing time variability and random machine breakdowns in a job shop environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 26-38, February.
    4. Rego, César & Duarte, Renato, 2009. "A filter-and-fan approach to the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 194(3), pages 650-662, May.
    5. Bürgy, Reinhard & Bülbül, Kerem, 2018. "The job shop scheduling problem with convex costs," European Journal of Operational Research, Elsevier, vol. 268(1), pages 82-100.
    6. Wei Xiong & Dongmei Fu, 2018. "A new immune multi-agent system for the flexible job shop scheduling problem," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 857-873, April.
    7. Zoghby, Jeriad & Wesley Barnes, J. & Hasenbein, John J., 2005. "Modeling the reentrant job shop scheduling problem with setups for metaheuristic searches," European Journal of Operational Research, Elsevier, vol. 167(2), pages 336-348, December.
    8. Valls, Vicente & Angeles Perez, M. & Sacramento Quintanilla, M., 1998. "A tabu search approach to machine scheduling," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 277-300, April.
    9. Carlo Mannino & Alessandro Mascis, 2009. "Optimal Real-Time Traffic Control in Metro Stations," Operations Research, INFORMS, vol. 57(4), pages 1026-1039, August.
    10. Guinet, Alain & Legrand, Marie, 1998. "Reduction of job-shop problems to flow-shop problems with precedence constraints," European Journal of Operational Research, Elsevier, vol. 109(1), pages 96-110, August.
    11. Leutwiler, Florin & Corman, Francesco, 2022. "A logic-based Benders decomposition for microscopic railway timetable planning," European Journal of Operational Research, Elsevier, vol. 303(2), pages 525-540.
    12. Michael Pinedo & Marcos Singer, 1999. "A shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 1-17, February.
    13. Yuri N. Sotskov, 2020. "Mixed Graph Colorings: A Historical Review," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    14. Amaral Armentano, Vinicius & Rigao Scrich, Cintia, 2000. "Tabu search for minimizing total tardiness in a job shop," International Journal of Production Economics, Elsevier, vol. 63(2), pages 131-140, January.
    15. Sándor Szabó, 2021. "A Clique Search Problem and its Application to Machine Scheduling," SN Operations Research Forum, Springer, vol. 2(4), pages 1-12, December.
    16. Kolisch, Rainer & Padman, Rema, 1997. "An integrated survey of project scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 463, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    17. Mascis, Alessandro & Pacciarelli, Dario, 2002. "Job-shop scheduling with blocking and no-wait constraints," European Journal of Operational Research, Elsevier, vol. 143(3), pages 498-517, December.
    18. Pezzella, Ferdinando & Merelli, Emanuela, 2000. "A tabu search method guided by shifting bottleneck for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 120(2), pages 297-310, January.
    19. Egon Balas & Alkis Vazacopoulos, 1998. "Guided Local Search with Shifting Bottleneck for Job Shop Scheduling," Management Science, INFORMS, vol. 44(2), pages 262-275, February.
    20. Yanwei Sang & Jianping Tan, 2022. "Many-Objective Flexible Job Shop Scheduling Problem with Green Consideration," Energies, MDPI, vol. 15(5), pages 1-17, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:45:y:1997:i:1:p:145-160. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.