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Unifying two Graph Decompositions with Modular Decomposition

Binh-Minh Bui-Xuan·Michel Habib·Vincent Limouzy·Fabien De Montgolfier
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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.

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Binh-Minh Bui-Xuan, Michel Habib, Vincent Limouzy, Fabien De Montgolfier. 2007-06-26. Unifying two Graph Decompositions with Modular Decomposition. https://doi.org/10.1007/978-3-540-77120-3

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