Covers in 4-uniform Intersecting Families with Covering Number Three

Shuya Chiba, Michitaka Furuya, Ryota Matsubara, Masanori Takatou

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1 Citation (Scopus)


Let k be an integer. In [3,4], Frankl, Ota and Tokushige proved that the maximum number of three-covers of a k-uniform intersecting family with covering number three is k3 - 3k2 + 6k - 4 for k = 3 or k ≥ 9, but the case 4 ≤ it ≤ 8 remained open. In this paper, we prove that the same holds for k = 4, and show that a 4-uniform family with covering number three which has 36 three-covers is uniquely determined.

Original languageEnglish
Pages (from-to)241-251
Number of pages11
JournalTokyo Journal of Mathematics
Issue number1
Publication statusPublished - 2012 Jun 1



  • Covering number
  • Intersecting family

ASJC Scopus subject areas

  • Mathematics(all)

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