A construction of almost Steiner systems

Asaf Ferber, Rani Hod, Michael Krivelevich, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

Abstract

Let n, k, and t be integers satisfying n > k > t ≥ 2. A Steiner system with parameters t, k, and n is a k-uniform hypergraph on n vertices in which every set of t distinct vertices is contained in exactly one edge. An outstanding problem in Design Theory is to determine whether a nontrivial Steiner system exists for t ≥ 6. In this note we prove that for every k > t ≥ 2 and sufficiently large n, there exists an almost Steiner system with parameters t, k, and n; that is, there exists a k-uniform hypergraph on n vertices such that every set of t distinct vertices is covered by either one or two edges.

Original languageEnglish
Pages (from-to)488-494
Number of pages7
JournalJournal of Combinatorial Designs
Volume22
Issue number11
DOIs
StatePublished - Nov 2014

Keywords

  • Steiner systems

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