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Codes et jeux de soustraction et de poursuite dans les graphes

Pierre Coupechoux 1
1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Identifying codes were introduced in 1998 by Karpovsky, Chakrabarty and Levitin. An identifying code is a subgraph such that each vertex is uniquely identified by the vertices in its neighborhood. There are several variants of these codes, including a colored version where the vertices are identified by the colors in their neighborhood. In this phd, we want to build an identifying coloring of a large cycle, given a fixed number of colors. We also studied identified codes in a certain class of oriented graphs: tournaments. We have also studied some topics in the game theory. The first one is a generalization of octal games, where we play on a graph instead of a heap. More precisely, the 0.33 game; each player can remove one or two vertices in a graph, with no disconnection allowed. The first player who cannot play loses. We studied this game in some graph classes: subdivided stars and subdivided bistars. The other game is called the Firefighter game. It's a one player game, where this one wants to contain a spreading fire in a graph. We solved a conjecture about this game, and introduced the online version of the game, for which we found some approximation results.
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Pierre Coupechoux. Codes et jeux de soustraction et de poursuite dans les graphes. Informatique et théorie des jeux [cs.GT]. INSA de Toulouse, 2018. Français. ⟨NNT : 2018ISAT0016⟩. ⟨tel-01946975v2⟩

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