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arXiv · 2007.02975

Negligible obstructions and Turán exponents

Tao Jiang·Zilin Jiang·Jie Ma
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Abstract

We show that for every rational number $r \in (1,2)$ of the form $2 - a/b$, where $a, b \in \mathbb{N}^+$ satisfy $\lfloor b/a \rfloor^3 \le a \le b / (\lfloor b/a \rfloor +1) + 1$, there exists a graph $F_r$ such that the Turán number $\operatorname{ex}(n, F_r) = Θ(n^r)$. Our result in particular generates infinitely many new Turán exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture.

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Tao Jiang, Zilin Jiang, Jie Ma. 2023-01-30. Negligible obstructions and Turán exponents. https://doi.org/10.4208/aam.oa-2022-0008

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