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On defect sets in bipartite graphs (extended abstract)

  • Session 7B
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Algorithms and Computation (ISAAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1350))

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Abstract

A defect set in a bipartite graph with vertex classes V and W is a subset X ⊂ V such that the neighbourhood N(X) satisfies |N(X)| < |X|. We study a lemma on defect sets in bipartite graphs with certain expanding properties from the algorithmic complexity point of view. This lemma is the core of a result of Friedman and Pippenger which states that expanding graphs contain all small trees. We also discuss related problems of finding shortest circuits of matroids represented over a field. In particular, we propose a new straightforward method to derive a weaker form (PR-completeness) of the recent NP-completeness results of Khachiyan [11] and Vardy [18] concerning this problem for the field of rationals and GF(p m), respectively.

The first author was partially supported by NSERC.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    P. E. Haxell

  2. Department of Applied Mathematics, Charles University, Prague, Czech Republic

    M. Loebl

Authors
  1. P. E. Haxell
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  2. M. Loebl
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Hon Wai Leong Hiroshi Imai Sanjay Jain

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© 1997 Springer-Verlag Berlin Heidelberg

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Haxell, P.E., Loebl, M. (1997). On defect sets in bipartite graphs (extended abstract). In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_36

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  • DOI: https://doi.org/10.1007/3-540-63890-3_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63890-2

  • Online ISBN: 978-3-540-69662-9

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