Uniform Intersecting Families with Covering Number Restrictions

P. Frankl, Katsuhiro Ota, N. Tokushige

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

It is known that any k-uniform family with covering number t has at most kt t-covers. In this paper, we deal with intersecting families and give better upper bounds for the number of t-covers. Let pt(k) be the maximum number of t-covers in any k-uniform intersecting families with covering number t. We prove that, for a fixed t, pt(k) ≤ kt - 1/√2 ⌊t-1/2⌋3/2kt-1 + O(kt-2). In the cases of t = 4 and 5, we also prove that the coefficient of kt-1 in pt(k) is exactly (t 2).

Original languageEnglish
Pages (from-to)47-56
Number of pages10
JournalCombinatorics Probability and Computing
Volume7
Issue number1
Publication statusPublished - 1998

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Intersecting Family
Covering number
Cover
Restriction
Upper bound
Coefficient

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Theoretical Computer Science

Cite this

Uniform Intersecting Families with Covering Number Restrictions. / Frankl, P.; Ota, Katsuhiro; Tokushige, N.

In: Combinatorics Probability and Computing, Vol. 7, No. 1, 1998, p. 47-56.

Research output: Contribution to journalArticle

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