Pleins étiquetages et configurations équilibrées : aspects topologiques de l'Optimisation Combinatoire

Frédéric Meunier 1
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : The main goal of this thesis is to develop combinatorial and constructive versions of some theorems in combinatorial optimization necessitating tools from algebraic topology. Generalizations of Sperner's lemma and Ky Fan's combinatorial formulae are proposed, as well as applications to the colorings of Kneser graphs and to the famous splitting necklace theorem. A scheduling problem, which has some common aspects with this last theorem, is treated as well. Finally, the last chapter contains new results concerning sigma-games (lights out games) on the grid.
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Frédéric Meunier. Pleins étiquetages et configurations équilibrées : aspects topologiques de l'Optimisation Combinatoire. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2006. Français. ⟨tel-00136938⟩

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