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C. Mathieu and . Décompositions-de-graphes, quelques limites et obstructions Résumé : Les décompositions de graphes, lorsqu'elles sont de petite largeur, sont souvent utilisées pour résoudre plus efficacement des problèmes étant difficiles dans le cas de graphes quelconques, ce travail de thèse, nous nous intéressons aux limites liées à ces décompositions

. Dans-une-première-partie, nous donnons un algorithme généralisant et unifiant la construction d'obstructions pour différentes largeurs de graphes, en temps XP lorsque paramétré par la largeur considérée. Nous obtenons en particulier le premier algorithme permettant de construire efficacement une obstruction à la largeur arborescente en temps O(n tw+4

. Dans-la-dernière-partie, nous étudions la complexité d'un nouveau problème de coloration appelé k-COLORATION ADDITIVE, combinant théorie des graphes et théorie des nombres. Nous montrons que ce nouveau problème est NP-complet pour tout k ? 4 fixé

. First, we give a generic algorithm unifying obstructions' construction for several graph widths, in XP time when parameterized by the considered width. In particular, it gives the first algorithm computing efficiently an obstruction to tree-width in time O

. Finally, we study the computational complexity of a new coloration problem, named k- ADDITIVE COLORING, which combines both graph theory and number theory. We show that this new problem is NP-complete for any fixed number k ? 4, while it can be solved in polynomial time on trees for any k