论文标题
微不足道的障碍物和Turán指数
Negligible obstructions and Turán exponents
论文作者
论文摘要
我们表明，对于$ 2- a/b $的（1,2）$的每个有理数$ r \ in $ a，b \ in \ mathbb {n}^ +$满足$ \ lfloor b/a \ rfloor^3 \ le a \ le a \ le a \ le a \ le a \ lfloor b/a \ lfloor b/a $ a $ a \ rfloor +rfloor +rfloor +rfloor +1 $ 1 +1 $ 1， Turán编号$ \ operatoTorname {ex}（n，f_r）=θ（n^r）$。我们的结果尤其产生了许多新的Turán指数。作为副产品，我们制定了一个在Bukh--Conlon猜想的工作中正在形成的框架。
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.
