On maximal intersecting families of finite sets

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Let r be a positive integer. A finite family H of pairwise intersecting r-sets is a maximal clique of order r, if for any set A ∉ H, |A| ≤ r there exists a member E ε{lunate} H such that A ∩ E = {circled division slash}. For instance, a finite projective plane of order r - 1 is a maximal clique. Let N(r) denote the minimum number of sets in a maximal clique of order r. We prove N(r) ≤ 3 4r2 whenever a projective plane of order r 2 exists. This disproves the known conjecture N(r) ≥ r2 - r + 1.

Original language English 282-289 8 Journal of Combinatorial Theory, Series A 28 3 https://doi.org/10.1016/0097-3165(80)90071-0 Published - 1980

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Intersecting Family
Maximal Clique
Finite Set
Finite projective plane
Disprove
Projective plane
Pairwise
Division
Denote
Integer

ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

Cite this

In: Journal of Combinatorial Theory, Series A, Vol. 28, No. 3, 1980, p. 282-289.

Research output: Contribution to journalArticle

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