Negligible obstructions and Turán exponents

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 $\mathrm{ex}(n,F_r)=\Theta (n^r)$. 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.

arXiv comment23 pages, 5 figures, published in Annals of Applied Mathematics

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