Covers in 4-uniform Intersecting Families with Covering Number Three

Shuya Chiba, Michitaka Furuya, Ryota Matsubara, Masanori Takatou

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume35
Issue number1
DOIs
Publication statusPublished - 2012 Jun

Keywords

  • Covering number
  • Intersecting family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Covers in 4-uniform Intersecting Families with Covering Number Three. / Chiba, Shuya; Furuya, Michitaka; Matsubara, Ryota; Takatou, Masanori.

In: Tokyo Journal of Mathematics, Vol. 35, No. 1, 06.2012, p. 241-251.

Research output: Contribution to journalArticle

Chiba, Shuya ; Furuya, Michitaka ; Matsubara, Ryota ; Takatou, Masanori. / Covers in 4-uniform Intersecting Families with Covering Number Three. In: Tokyo Journal of Mathematics. 2012 ; Vol. 35, No. 1. pp. 241-251.
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