Hypergraphs with arbitrarily small codegree Turán density

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2026-03-27 DOI:10.1112/blms.70348

Simón Piga, Bjarne Schülke

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引用次数: 0

Abstract

The codegree Turán density $γ (F)$ of a $k$ -graph $F$ is the smallest $γ \in [0, 1)$ such that every $k$ -graph $H$ with $δ_{k - 1} (H) ⩾ (γ + o (1)) | V (H) |$ contains a copy of $F$ . In this work, we show that for every $ε > 0$ , there is a $k$ -uniform hypergraph $F$ with $0 < γ (F) < ε$ . The initial preprint of this work leads to significant subsequent research on accumulation points of variants of the Turán density.

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具有任意小余度Turán密度的超图

k $k$ -图F $F$的余度Turán密度γ (F) $\gamma (F)$是最小的γ∈[0]1) $\gamma \in [0,1)$使得每k $k$ -图H $H$ δ k−1(H)小于（γ + 0 (1)）| V (H) | $\delta _{k-1}(H)\geqslant (\gamma +o(1))\vert V(H)\vert$包含F $F$的副本。在这项工作中，我们证明了对于每一个ε ＆gt； 0 $\varepsilon >0$，存在一个具有0 ＆lt； γ (F) ＆lt; ε $0<\gamma (F)<\varepsilon$的k $k$ -一致超图F $F$。这项工作的最初预印本导致了对Turán密度变体积累点的重要后续研究。

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