Wickets in 3-uniform Hypergraphs

2023/05/02 by József Solymosi, Solymosi, Jozsef
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.01193

openalex publication_date 2023/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In these notes, we consider a Turán-type problem in hypergraphs. What is the maximum number of edges if we forbid a subgraph? Let H_n⁽³⁾ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, called \em wicket, is formed by three rows and two columns of a 3 × 3 point matrix. We describe two linear hypergraphs -- both containing a wicket -- that if we forbid either of them in H_n⁽³⁾, then the hypergraph is sparse, and the number of its edges is o(n²). This proves a conjecture of Gyárfás and Sárközy.

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