Decomposition Theorems for Square-free 2-matchings in Bipartite Graphs

  • Kenjiro TakazawaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)


A square-free 2-matching in an undirected graph is a simple 2-matching without cycles of length four. In bipartite graphs, the maximum square-free 2-matching problem is well-solved. Previous results include min-max theorems, polynomial combinatorial algorithms, polyhedral description with dual integrality, and discrete convex structure.

In this paper, we further investigate the structure of square-free 2-matchings in bipartite graphs to present new decomposition theorems, which serve as an analogue of the Dulmage-Mendelsohn decomposition for bipartite matchings and the Edmonds-Gallai decomposition for nonbipartite matchings. We exhibit two canonical minimizers of the set function in the min-max formula, and a characterization of the maximum square-free 2-matchings with the aid of these canonical minimizers.


Matching theory Square-free 2-matching Dulmage-Mendelsohn decomposition Edmonds-Gallai decomposition 



The author is thankful to Satoru Iwata for suggesting this research and Zoltán Király for informing him of the history of the two min-max theorems for the maximum square-free 2-matching problem in bipartite graphs. This work is partially supported by JSPS KAKENHI Grant Numbers 25280004 and 26280001.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Industrial and Systems Engineering, Faculty of Science and EngineeringHosei UniversityTokyoJapan

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