On a graph coloring problem arising from discrete tomography

An extension of the basic image reconstruction problem in discrete tomography is considered: given a graph G = (V, E) and a family P of chains Pi together with vectors h(Pi) = (h 1 i , ..., h k i ), one wants to find a partition V , ..., V k of V such that for each Pi and each color j, |V ∩Pi| = hji . 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 V , ..., V k 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.