Graph coloring with cardinality constraints on the neighborhoods

Abstract : Extensions and variations of the basic problem of graph coloring are introduced. It consists essentially in finding in a graph G a k-coloring, i.e., a partition V 1, ..., V k of the vertex set of G such that for some specified neighborhood ˜N (v) of each vertex v, the number of vertices in ˜N (v) \ V i is (at most) a given integer hi v. The complexity of some variations is discussed according to ˜N (v) which may be the usual neighbors, or the vertices at distance at most 2 or the closed neighborhood of v (v and its neighbors). Polynomially solvable cases are exhibited (in particular when G is a special tree).
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Submitted on : Tuesday, April 8, 2014 - 2:49:11 PM
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Marie-Christine Costa, Dominique de Werra, Christophe Picouleau, Bernard Ries. Graph coloring with cardinality constraints on the neighborhoods. Discrete Optimization, Elsevier, 2009, 6 (4), pp.362--369. ⟨10.1016/j.disopt.2009.04.005⟩. ⟨hal-00975361⟩

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