Random Turán Problems for K_s,t Expansions

2024/12/12 by Jiaxi Nie, Nie, Jiaxi, Sam Spiro +1 · 1 citation
Economics, Econometrics and Finance · #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2412.09367

openalex publication_date 2024/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K_s,t^(r) denote the r-uniform hypergraph obtained from the graph K_s,t by inserting r-2 new vertices inside each edge of K_s,t. We prove essentially tight bounds on the size of a largest K_s,t^(r)-subgraph of the random r-uniform hypergraph G_n,p^r whenever r≥ 2s/3+2, giving the first random Turán results for expansions that go beyond a natural "tight-tree barrier." In addition to this, our methods yield optimal supersaturation results for K_s,t⁽³⁾ for sufficiently dense host hypergraphs, which may be of independent interest.

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