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On the expansion of combinatorial polytopes

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Mathematical Foundations of Computer Science 1992 (MFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 629))

Abstract

Strong expansion properties have been established fot several classes of graphs that can be expressed as the 1-skeletons of 0–1 polytopes. These include graphs associated with, matchings, older ideals, independent sets, and balanced matroids (e.g. for the graphic matroid). The question whether these are examples of a more general phenomenon has been raizeD: “Do all 0–1 polytopes have cutset expansion at least 1 ?” A positive answer to the above question (even in weaker or more special form), implies efficient randomized algorithms to approximate a vast class of N P-hard counting problems.

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Authors and Affiliations

  1. Bell Communications Research, 445 South Street, 07960, Morristown, NJ

    Milena Mihail

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  1. Milena Mihail
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Ivan M. Havel Václav Koubek

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© 1992 Springer-Verlag Berlin Heidelberg

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Mihail, M. (1992). On the expansion of combinatorial polytopes. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_4

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  • DOI: https://doi.org/10.1007/3-540-55808-X_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55808-8

  • Online ISBN: 978-3-540-47291-9

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