The Brown-Erdős-Sós Conjecture for hypergraphs of large uniformity

2020/07/29 by Peter Keevash, Keevash, Peter, Jason Long +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2007.14824

openalex publication_date 2020/07/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We prove the well-known Brown-Erdős-Sós Conjecture for hypergraphs of large uniformity in the following form: any dense linear r-graph G has k edges spanning at most (r-2)k+3 vertices, provided the uniformity r of G is large enough given the linear density of G, and the number of vertices of G is large enough given r and k.

Citations

• The existence of designs
• On Certain Sets of Integers
• On a conjecture of Erdős on locally sparse Steiner triple systems
• A New Bound for the Brown--Erdős--Sós Problem

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