Unifying Two Graph Decompositions with Modular Decomposition

We introduces the umodules, a generalization 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.

• Type: Conference
• Year: 2007
• Where: ISAAC
• Authors: Binh-Minh Bui-Xuan, Michel Habib, Vincent Limouzy, Fabien de Montgolfier
• Keywords: Decomposition, Decomposition Tree, ISAAC 2007, Unique Decomposition Tree