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Remarks on an Edge Isoperimetric Problem

Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Adjacency Matrix Large Eigenvalue Discrete Math Degree Sequence Laplace Eigenvalue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • C. Bey

There are no affiliations available

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