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On Systems of Small Sets with No Large Δ-Subsystems

Published online by Cambridge University Press:  01 May 1999

A. V. KOSTOCHKA ,
V. RÖDL  and
L. A. TALYSHEVA
A. V. KOSTOCHKA
Affiliation:
Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk-90, 630090, Russia (e-mail: sasha@math.nsc.ru)
V. RÖDL
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA (e-mail: rodl@mathcs.emory.edu)
L. A. TALYSHEVA
Affiliation:
Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk-90, 630090, Russia (e-mail: sasha@math.nsc.ru)
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Abstract

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A family of k sets is called a Δ-system if any two sets have the same intersection. Denote by f(r, k) the least integer so that any r-uniform family of f(r, k) sets contains a Δ-system consisting of k sets. We prove that, for every fixed r, f(r, k) = kr + o(kr). Using a recent result of Molloy and Reed [5], a bound on the error term is provided for sufficiently large k.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 3 , May 1999 , pp. 265 - 268
Copyright
1999 Cambridge University Press