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On combinatorial properties of binary spaces

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Integer Programming and Combinatorial Optimization (IPCO 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

Abstract

A binary clutter is the family of inclusionwise minimal supports of vectors of affine spaces over GF(2). Binary clutters generalize various objects studied in Combinatorial Optimization, such as paths, Chinese Postman Tours, multiflows and one-sided circuits on surfaces. The present work establishes connections among three matroids associated with binary clutters, and between any of them and the binary clutter. These connections are then used to compare well-known classes of binary clutters; to provide polynomial algorithms which either confirm the membership in subclasses, or provide a forbidden clutter-minor; to reformulate and generalize a celebrated conjecture of Seymour on ideal binary clutters in terms of multiflows in matroids, and to exhibit new cases of its validity.

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Author information

Authors and Affiliations

  1. Clemson University, 29634-1907, Clemson, South Carolina, USA

    Beth Novick

  2. CNRS, IMAG, ARTEMIS, Université Fourier Grenoble 1, France

    András Sebő

Authors
  1. Beth Novick
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  2. András Sebő
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Editor information

Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Novick, B., Sebő, A. (1995). On combinatorial properties of binary spaces. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_53

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  • DOI: https://doi.org/10.1007/3-540-59408-6_53

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

  • eBook Packages: Springer Book Archive

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