A proof of Frankl-Kupavskii's conjecture on edge-union condition
Abstract
A 3-graph F is U(s, 2s+1) if for any s edges e1,...,es∈ E(F), |e1... es|≤ 2s+1. Frankl and Kupavskii (2020) proposed the following conjecture: For any 3-graph F with n vertices, if F is U(s, 2s+1), then e(F)≤ \n-1 2, (n-s-1)s+1 2+s+1 3, 2s+1 3\. In this paper, we confirm Frankl and Kupavskii's conjecture.
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