# Unifying Two Graph Decompositions with Modular Decomposition

Abstract : 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.
Document type :
Conference papers

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00325376
Contributor : Binh-Minh Bui-Xuan <>
Submitted on : Monday, September 29, 2008 - 10:15:00 AM
Last modification on : Friday, March 27, 2020 - 3:34:37 AM

### Citation

Binh-Minh Bui-Xuan, Michel Habib, Vincent Limouzy, Fabien de Montgolfier. Unifying Two Graph Decompositions with Modular Decomposition. ISAAC'07: 18th International Symposium on Algorithms and Computation, Dec 2007, Sendai, Japan. pp.52-64, ⟨10.1007/978-3-540-77120-3_7⟩. ⟨lirmm-00325376⟩

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