3,304 research outputs found
A cutting plane algorithm for graph coloring
AbstractWe present an approach based on integer programming formulations of the graph coloring problem. Our goal is to develop models that remove some symmetrical solutions obtained by color permutations. We study the problem from a polyhedral point of view and determine some families of facets of the 0/1-polytope associated with one of these integer programming formulations. The theoretical results described here are used to design an efficient Cutting Plane algorithm
A polyhedral approach for the Equitable Coloring Problem
In this work we study the polytope associated with a 0,1-integer programming
formulation for the Equitable Coloring Problem. We find several families of
valid inequalities and derive sufficient conditions in order to be
facet-defining inequalities. We also present computational evidence that shows
the efficacy of these inequalities used in a cutting-plane algorithm
Coloring half-planes and bottomless rectangles
We prove lower and upper bounds for the chromatic number of certain
hypergraphs defined by geometric regions. This problem has close relations to
conflict-free colorings. One of the most interesting type of regions to
consider for this problem is that of the axis-parallel rectangles. We
completely solve the problem for a special case of them, for bottomless
rectangles. We also give an almost complete answer for half-planes and pose
several open problems. Moreover we give efficient coloring algorithms
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