The turán number of berge-K 4 in triple systems

Research output: Contribution to journalArticle

Abstract

A Berge-K 4 in a triple system is a configuration with four vertices v1, v2, v3, v4 and six distinct triples { eij: 1 ≤ i < j ≤ 4} such that { vi, vj} ⊂ eij for every 1 ≤ i < j ≤ 4. We denote by B the set of Berge-K 4 configurations. A triple system is B-free if it does not contain any member of B. We prove that the maximum number of triples in a B -free triple system on n > 6 points is obtained by the balanced complete 3-partite triple system: all triples { abc : a ∈ A, b ∈ B, c ∈ C} where A,B,C is a partition of n points with ⌊ n/3⌋ = | A| ≤ |B| ≤ | C| = ⌈ n/3⌉.

Original language English 383-392 10 SIAM Journal on Discrete Mathematics 33 1 https://doi.org/10.1137/18M1204048 Published - Jan 1 2019

Triple System
Configuration
Partition
Denote
Distinct

Keywords

• Berge-G hypergraphs
• Triple system
• Turán number

ASJC Scopus subject areas

• Mathematics(all)

Cite this

In: SIAM Journal on Discrete Mathematics, Vol. 33, No. 1, 01.01.2019, p. 383-392.

Research output: Contribution to journalArticle

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