The maximum of the product of nontrivial cross-intersecting 3-graphs

Let $𝒜, ℬ \subset (\binom{[n]}{3})$ be nontrivial cross-intersecting $3$ -graphs. That is, $⋂_{A \in 𝒜} A = \emptyset = ⋂_{B \in ℬ} B$ and $A \cap B \neq \emptyset$ for all $A \in 𝒜$ , $B \in ℬ$ . The best possible upper bound $| 𝒜 | | ℬ | \leq {(3 n - 8)}^{2}$ is established for $n \geq 6$ .

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Keywords

hypergraphs, extremal problems, intersection

Mathematical Subject Classification

Primary: 05D05

Secondary: 05C65

Milestones

Received: 29 September 2025

Revised: 8 November 2025

Accepted: 24 November 2025

Published: 17 December 2025

Authors

Peter Frankl
Renyi Institute Hungarian Academy of Sciences Budapest Hungary

Vol. 15, No. 1, 2026

Peter Frankl

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors