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Laboratoire d'Informatique Algorithmique, Fondements et Applications |  |
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Laboratoire d'Informatique Algorithmique, Fondements et Applications | |
| HAL: lirmm-00325376, version 1 |
| DOI: 10.1007/978-3-540-77120-3_7 |
| Detailed view |  Export this paper |
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| ISAAC'07: 18th International Symposium on Algorithms and Computation, Sendai, Japan : (2007) |
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| Unifying Two Graph Decompositions with Modular Decomposition |
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| Binh-Minh Bui-Xuan 1Michel Habib 2 |
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| (2007-12-06) |
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| We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomial-time algorithms are provided for: non-trivial umodule test, maximal umodule computation, and decomposition tree computation when the tree exists. Our results unify many known decomposition like modular and bi-join decomposition of graphs, and a new decomposition of tournaments. |
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| 1: | Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM) |
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CNRS : UMR5506 – Université Montpellier II - Sciences et techniques |
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| 2: | Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA) |
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CNRS : UMR7089 – Université Paris VII - Paris Diderot |
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| Subject | : | Computer Science/Discrete Mathematics |
| lirmm-00325376, version 1 | |
| http://hal-lirmm.ccsd.cnrs.fr/lirmm-00325376 | |
| oai:hal-lirmm.ccsd.cnrs.fr:lirmm-00325376 | |
| From: Binh-Minh Bui-Xuan | |
| Submitted on: Monday, 29 September 2008 10:15:00 | |
| Updated on: Monday, 6 October 2008 15:23:19 | |
