Unifying two Graph Decompositions with Modular Decomposition

Binh-Minh Bui-Xuan (1) , Michel Habib (2) , Vincent Limouzy (2) , Fabien de Montgolfier (2)

1 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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.

Mots clés: Algorithms; Umodule; Modular Decomposition; Graph; Discrete Structures; Tournaments decomposition

Domaines: Algorithme et structure de données [cs.DS]

Binh-Minh Bui-Xuan, Michel Habib, Vincent Limouzy, Fabien de Montgolfier. Unifying two Graph Decompositions with Modular Decomposition. International Symposium on Algorithms and Computation (ISAAC, Dec 2007, Sendai, Japan. pp.52-64, ⟨10.1007/978-3-540-77120-3⟩. ⟨hal-00022957v3⟩