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Theses

Indécomposabilité des graphes et des tournois

Abstract : This thesis focuses on indecomposability in graphs and tournaments. It contains five chapters, The first is introductory. The second chapter is a study of indecomposable tournaments according to the indecomposable subtournaments on 5 or 7 vertices embedding in. The third chapter is a characterization of the (-1)-critical tournaments. The fourth chapter contains a characterization of the (-1)-critical graphs answering in the general case, to a problem asked by Y. Boudabbous and P. Ille. The fifth chapter is devoted to an inversion operation in tournaments and an invariant, the inversion index of a tournament, which the study was proposed by M. Pouzet. The fact that the inversion index of a (-1)-critical tournament is between 2 and 4 is the link with the study of criticality. Many properties of the class of tournaments with inversion index at most n are given
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Houmem Belkhechine. Indécomposabilité des graphes et des tournois. Mathématiques générales [math.GM]. Université Claude Bernard - Lyon I; Université de Sfax. Faculté des sciences, 2009. Français. ⟨NNT : 2009LYO10115⟩. ⟨tel-00609544⟩

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