Unavoidable subhypergraphs: a-clusters

Zoltán Füredi, Lale Özkahya

Research output: Contribution to journalArticle

2 Citations (Scopus)


One of the central problems of extremal hypergraph theory is the description of unavoidable subhypergraphs, in other words, the Turan problem. Let a = (a1, ..., ap) be a sequence of positive integers, p ≥ 2, k = a1 + ... + ap. An a-cluster is a family of k-sets {F0, ..., Fp} such that the sets Fi \ F0 are pairwise disjoint (1 ≤ i ≤ p), | Fi \ F0 | = ai, and the sets F0 \ Fi are pairwise disjoint, too. Given a there is a unique a-cluster, and the sets F0 \ Fi form an a-partition of F0. With an intensive use of the delta-system method we prove that for k > p > 1 and sufficiently large n, (n > n0 (k)), if F is an n-vertex k-uniform family with | F | exceeding the Erdo{combining double acute accent}s-Ko-Rado bound ((n - 1; k - 1)), then F contains an a-cluster. The only extremal family consists of all the k-subsets containing a given element.

Original languageEnglish
Pages (from-to)63-67
Number of pages5
JournalElectronic Notes in Discrete Mathematics
Publication statusPublished - Aug 1 2009


  • Erdo{combining double acute accent}s-Ko-Rado
  • set systems
  • traces

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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