Abstract
In this work we consider the distance model for the classical vertex coloring problem, introduced by Delle Donne in 2009. This formulation involves decision variables representing the distance between the colors assigned to every pair of distinct vertices, thus not explicitly representing the colors assigned to each vertex. We show close relations between this formulation and the so-called orientation model for graph coloring. In particular, we prove that we can translate many facet-inducing inequalities for the orientation model polytope into facet-inducing inequalities for the distance model polytope, and viceversa.
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Dias, B., de Freitas, R., Maculan, N., Marenco, J. (2018). The Distance Polytope for the Vertex Coloring Problem. In: Lee, J., Rinaldi, G., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science(), vol 10856. Springer, Cham. https://doi.org/10.1007/978-3-319-96151-4_13
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DOI: https://doi.org/10.1007/978-3-319-96151-4_13
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