Geodesic
Degree-constrained edge partitioning in graphs arising from discrete tomography
Journal of Graph Algorithms and Applications, Tome 13 (2009) no. 2, pp. 99-118.

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Starting from the basic problem of reconstructing a 2-dimensional image 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 specified vertices. A variation where the graph is oriented is also presented. In addition we explore similar problems for the case where the underlying graph is a complete graph (instead of a complete bipartite graph). 
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     author = {Cedric Bentz and Marie-Christine Costa and Christophe Picouleau and Bernard Ries and Dominique de Werra},
     title = {Degree-constrained edge partitioning in graphs 
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     journal = {Journal of Graph Algorithms and Applications},
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     doi = {10.7155/jgaa.00178},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00178/}
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Cedric Bentz; Marie-Christine Costa; Christophe Picouleau; Bernard Ries; Dominique de Werra. Degree-constrained edge partitioning in graphs 
arising from discrete tomography. Journal of Graph Algorithms and Applications, Tome 13 (2009) no. 2, pp. 99-118. doi : 10.7155/jgaa.00178. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00178/

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