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General Theory of Information Transfer and Combinatorics pp 971–978Cite as

Remarks on an Edge Isoperimetric Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

Among all collections of a given number of k-element subsets of an n-element groundset find a collection which maximizes the number of pairs of subsets which intersect in k–1 elements.

This problem was solved for k=2 by Ahlswede and Katona, and is open for k>2.

We survey some linear algebra approaches which yield to estimations for the maximum number of pairs, and we present another short proof of the Ahlswede-Katona result.

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Authors
  1. C. Bey
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    Rudolf Ahlswede

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Lars Bäumer , Ning Cai , Harout Aydinian  & Christian Deppe , ,  & 

  3. Russian Academy of Sciences Institute of Problems of Information Transmission, Bol’shoi Karetnyi per. 19, 101447, Moscow, Russia

    Vladimir Blinovsky

  4. Universität Bielefeld, Fakultät für Mathematik, Universitätsstr. 25, 33615, Bielefeld, Germany

    Haik Mashurian

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© 2006 Springer-Verlag Berlin Heidelberg

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Bey, C. (2006). Remarks on an Edge Isoperimetric Problem. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_62

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  • DOI: https://doi.org/10.1007/11889342_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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