Graph Coloring and Graph Convexity

Julio Araujo 1, 2
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : In this thesis, we study several problems of Graph Theory concerning Graph Coloring and Graph Convexity. Most of the results contained here are related to the computational complexity of these problems for particular graph classes. In the rst and main part of this thesis, we deal with Graph Coloring which is one of the most studied areas of Graph Theory. We rst consider three graph coloring problems called Greedy Coloring, Weighted Coloring and Weighted Improper Coloring. Then, we deal with a decision problem, called Good Edge-Labeling, whose de nition was motivated by the Wavelength Assignment problem in optical networks. The second part of this thesis is devoted to a graph optimization parameter called (geodetic) hull number. The de nition of this parameter is motivated by an extension to graphs of the notions of convex sets and convex hulls in the Euclidean space. Finally, we present in the appendix other works developed during this thesis, one about Eulerian and Hamiltonian directed hypergraphs and the other concerning distributed storage systems.
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Submitted on : Monday, September 17, 2012 - 1:46:37 PM
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Julio Araujo. Graph Coloring and Graph Convexity. Computational Complexity [cs.CC]. Université Nice Sophia Antipolis, 2012. English. ⟨tel-00732919⟩

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