Degree-constrained edge partitioning in graphs arising from discrete tomography

Abstract : 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 specified 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).
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Submitted on : Tuesday, April 8, 2014 - 2:31:59 PM
Last modification on : Thursday, October 10, 2019 - 10:34:04 AM

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Cédric 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, Brown University, 2009, 13 (2), pp.99-118. ⟨10.7155/jgaa.00178⟩. ⟨hal-00975345⟩

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