Bimodular decomposition of bipartite graphs

Authors:
Jean-Luc Fouquet;Michel Habib;Fabien de Montgolfier;Jean-Marie Vanherpe
Affiliations:
Université du Maine;LIRMM, Université Montpellier II;LIAFA, Université Paris 7;Université du Maine
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

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Abstract

This paper gives a decomposition theory for bipartite graphs. It uses bimodules, a special case of 2-modules (also known as homogeneous pairs, an extension of both modules and splits). It is shown how a unique decomposition tree represents the bimodular decomposition of a bipartite graph, with strong analogs with modular decomposition of graphs. An O(mn3) algorithm for this decomposition is provided. At least a classification of the 2-modules of a bipartite graph is given.