, Volume 19, Issue 4, pp 404–433 | Cite as

Graph coloring inequalities from all-different systems

  • David Bergman
  • J. N. Hooker


We explore the idea of obtaining valid inequalities for a 0–1 model from a finite-domain constraint programming formulation of the problem. In particular, we formulate a graph coloring problem as a system of all-different constraints. By analyzing the polyhedral structure of all-different systems, we obtain facet-defining inequalities that can be mapped to valid cuts in the classical 0–1 model of the problem. We focus on cuts corresponding to cycles and webs and show that they are stronger than known cuts for these structures. We also identify path cuts and show they do not strengthen the bound. Computational experiments for a set of benchmark instances reveal that finite-domain cycle cuts often deliver tighter bounds, in less time, than classical 0–1 cuts.


Graph coloring Finite-domain variables Facet-defining inequalities 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of BusinessUniversity of ConnecticutStamfordUSA
  2. 2.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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