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Facets of the Graph Coloring Polytope

Author

Listed:
  • Pablo Coll
  • Javier Marenco
  • Isabel Méndez Díaz
  • Paula Zabala

Abstract

In this paper we present a study of the polytope associated to a classic linear integer programming formulation of the graph coloring problem. We determine some families of facets. This is the initial step for the development of a branch-and-cut algorithm to solve large instances of the graph coloring problem. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Pablo Coll & Javier Marenco & Isabel Méndez Díaz & Paula Zabala, 2002. "Facets of the Graph Coloring Polytope," Annals of Operations Research, Springer, vol. 116(1), pages 79-90, October.
    • Handle: RePEc:spr:annopr:v:116:y:2002:i:1:p:79-90:10.1023/a:1021315911306
    DOI: 10.1023/A:1021315911306
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    Citations

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    Cited by:

    1. Stefano Gualandi & Federico Malucelli, 2012. "Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 81-100, February.
    2. Adolfo R. Escobedo & Romena Yasmin, 2023. "Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures," Journal of Combinatorial Optimization, Springer, vol. 46(3), pages 1-45, October.
    3. Fabrizio Borghini & Isabel Méndez-Díaz & Paula Zabala, 2020. "An exact algorithm for the edge coloring by total labeling problem," Annals of Operations Research, Springer, vol. 286(1), pages 11-31, March.
    4. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2010. "A supernodal formulation of vertex colouring with applications in course timetabling," Annals of Operations Research, Springer, vol. 179(1), pages 105-130, September.
    5. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2012. "A branch-and-cut procedure for the Udine Course Timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 71-87, April.

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