An exact extremal result for tournaments and 4-uniform hypergraphs

2018/02/21 by Wiam Belkouche, Belkouche, Wiam, Abderrahim Boussaïri +5
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1802.07621

openalex publication_date 2018/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we address the following problem due to Frankl and Füredi (1984). What is the maximum number of hyperedges in an r-uniform hypergraph with n vertices, such that every set of r+1 vertices contains 0 or exactly 2 hyperedges? They solved this problem for r=3. For r=4, a partial solution is given by Gunderson and Semeraro (2017) when n=q+1 for some prime power number q≡3\pmod4 . Assuming the existence of skew-symmetric conference matrices for every order divisible by 4, we give a solution for n≡0\pmod4 and for n≡3\pmod4.

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