Unifying two graph decompositions with modular decomposition

Authors:
Binh-Minh Bui-Xuan;Michel Habib;Vincent Limouzy;Fabien de Montgolfier
Affiliations:
LIRMM - Univ. Montpellier II;LIAFA - Univ. Paris Diderot;LIAFA - Univ. Paris Diderot;LIAFA - Univ. Paris Diderot
Venue:
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Year:
2007

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Abstract

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.