Hypergraphs without exponents

2019/06/16 by Zoltán Füredi, Füredi, Zoltán, Dániel Gerbner +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1906.06657

10 pages

arxiv created 2019/06/16 · arxiv updated 2019/06/18

Abstract

Here we give a short, concise proof for the following result. There exists a k-uniform hypergraph H (for k≥ 5) without exponent, i.e., when the Turán function is not polynomial in n. More precisely, we have ex(n,H)=o(n^k-1) but it exceeds n^k-1-c for any positive c for n> n₀(k,c). This is an extension (and simplification) of a result of Frankl and the first author from 1987 where the case k=5 was proven. We conjecture that it is true for k∈ \3, 4\ as well.

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