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The Square-Free 2-Factor Problem in Bipartite Graphs

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Book cover Integer Programming and Combinatorial Optimization (IPCO 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1610))

Abstract

The 2-factor problem is to find, in an undirected graph, a spanning subgraph whose components are all simple cycles; hence it is a relaxation of the problem of finding a Hamilton tour in a graph. In this paper we study, in bipartite graphs, a problem of intermediate difficulty: the problem of finding a 2-factor that contains no 4-cycles. We introduce a polynomial time algorithm for this problem; we also present an “augmenting path” theorem, a polyhedral characterization, and a “Tutte-type” characterization of the bipartite graphs that contain such 2-factors.

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Author information

Authors and Affiliations

  1. College of Business Administration, University of Notre Dame, P.O. Box 399, Notre Dame, IN, 46556-0399

    David Hartvigsen

Authors
  1. David Hartvigsen
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Editor information

Editors and Affiliations

  1. GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard  & Gerhard J. Woeginger  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Hartvigsen, D. (1999). The Square-Free 2-Factor Problem in Bipartite Graphs. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_18

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  • DOI: https://doi.org/10.1007/3-540-48777-8_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66019-4

  • Online ISBN: 978-3-540-48777-7

  • eBook Packages: Springer Book Archive

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