Corpus ID: 211096618

# A generalization of the K\H{o}v\'{a}ri-S\'{o}s-Tur\'{a}n theorem

@article{Geneson2020AGO,
title={A generalization of the K\H\{o\}v\'\{a\}ri-S\'\{o\}s-Tur\'\{a\}n theorem},
author={Jesse Geneson},
journal={arXiv: Combinatorics},
year={2020}
}
• Jesse Geneson
• Published 2020
• Mathematics, Computer Science
• arXiv: Combinatorics
• We present a new proof of the K\H{o}v\'{a}ri-S\'{o}s-Tur\'{a}n theorem that $ex(n, K_{s,t}) = O(n^{2-1/t})$ for $s, t \geq 2$. The new proof is elementary, avoiding the use of convexity. For any $d$-uniform hypergraph $H$, let $ex_d(n,H)$ be the maximum possible number of edges in an $H$-free $d$-uniform hypergraph on $n$ vertices. Let $K_{H, t}$ be the $(d+1)$-uniform hypergraph obtained from $H$ by adding $t$ new vertices $v_1, \dots, v_t$ and replacing every edge $e$ in $E(H)$ with $t$ edges… CONTINUE READING

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