Hypergraphs without exponents

[摘要] A short, concise proof is given for that for k >= 5 there exists a k-uniform hypergraph H without exponent, i.e., when the Turan 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 > n(0)(k, c). We conjecture that this is true for k is an element of{3, 4} as well. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Extremal hypergraph theory;Turan problem