## Degree-constrained edge partitioning in graphs arising from discrete tomography

### Bentz, Cédric ; Costa, Marie-Christine ; Picouleau, Christophe ; Ries, Bernard ; de Werra, Dominique

### In: Journal of Graph Algorithms and Applications, 2009, vol. 13, no. 2, p. 99-118

Starting from the basic problem of reconstructing a 2-dimensional im- age given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k = 3 colors is open. Variations and special cases are considered for the case k = 3 colors where the graph corresponding to the union of some color classes (for instance colors 1... More

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- Starting from the basic problem of reconstructing a 2-dimensional im- age given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k = 3 colors is open. Variations and special cases are considered for the case k = 3 colors where the graph corresponding to the union of some color classes (for instance colors 1 and 2) has a given structure (tree, vertex- disjoint chains, 2-factor, etc.). We also study special cases corresponding to the search of 2 edge-disjoint chains or cycles going through speci ed vertices. A variation where the graph is oriented is also presented. In addition we explore similar problems for the case where the under- lying graph is a complete graph (instead of a complete bipartite graph).