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On Systems of Small Sets with No Large Δ-Subsystems
Published online by Cambridge University Press: 01 May 1999
Abstract
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.
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- 1999 Cambridge University Press
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