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Theses

Décomposition algorithmique des graphes

Abstract : In this thesis, we study two graph decompositions introduced by Roberston and Seymour: the tree-decompositions and the branch-decompositions. Two graph parameters are associated to these decompositions: the treewidth and the branchwidth. We show how these decompositions can be united under a common combinatorial structure; both treewidth and branchwidth correspond to minimal values of parameters on this common structure. Using this parallel we adapt a general algorithm that computes the treewidth of some graphs to the branchwidth. We can apply this new algorithm to graphs of bounded asteroidal number with polynomial number of minimal separators and d-trapezoid circular graphs. We also use this analogy to adapt structural properties of branch-decompositions to tree-decompositions. In the case of planar graphs, we give a topological interpretation of these properties which leads us to a simple proof of a theorem linking the treewidth of a planar graph to the treewidth of its dual. Using this topological point of view, we also give an efficient algorithm to list the minimal separators of a planar graph.
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https://tel.archives-ouvertes.fr/tel-00148807
Contributor : Frédéric Mazoit <>
Submitted on : Wednesday, May 23, 2007 - 12:03:11 PM
Last modification on : Thursday, November 21, 2019 - 2:27:05 AM
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  • HAL Id : tel-00148807, version 1

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Frédéric Mazoit. Décomposition algorithmique des graphes. Mathématiques [math]. Ecole normale supérieure de lyon - ENS LYON, 2004. Français. ⟨tel-00148807⟩

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