Graph coloring with cardinality constraints on the neighborhoods
Discrete Optimization
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An extension of the basic image reconstruction problem in discrete tomography is considered: given a graph G = (V,E) and a family $\cal {P}$ of chains Pi together with vectors h(Pi) = (h i1,…,h ik), one wants to find a partition V1,…,Vk of V such that for each Pi and each color j, |Vj ∩ Pi| = h ij. An interpretation in terms of scheduling is presented. We consider special cases of graphs and identify polynomially solvable cases; general complexity results are established in this case and also in the case where V1,…,Vk is required to be a proper vertex k-coloring of G. Finally, we examine also the case of (proper) edge k-colorings and determine its complexity status. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008