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(mn 3) algorithm for this decomposition is provided. At least a classification of the 2-modules of a bipartite graph is given.
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Fouquet, JL., Habib, M., de Montgolfier, F., Vanherpe, JM. (2004). Bimodular Decomposition of Bipartite Graphs. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_10
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DOI: https://doi.org/10.1007/978-3-540-30559-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24132-4
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