Degree-constrained edge partitioning in graphs arising from discrete tomography

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, vertexdisjoint 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). Submitted: February 2007 Reviewed: September 2008 Revised: October 2008 Accepted: November 2008 Final: January 2009 Published: February 2009 Article type: Regular Paper Communicated by: L. Arge E-mail addresses: [email protected] (C. Bentz) [email protected] (M.-C. Costa) [email protected] (C. Picouleau) [email protected] (B. Ries) [email protected] (D. de Werra) 100 Bentz et al. Degree-constrained edge partitioning This paper is dedicated to H.J. Ryser in acknowledgement for his seminal work which stated the now famous Ryser conditions exactly 50 years ago.