论文标题
关于$ k_ {3，t} $的1-助图的Turán编号
On the Turán number of 1-subdivision of $K_{3,t}$
论文作者
论文摘要
对于图$ h $，由$ h'$表示的1个$ h $的1个分割是通过内部脱节的长度2替换$ h $获得的图形。最近，Conlon，Janzer，Janzer和Lee（Arxiv：1903.10631）问：以下问题：对于任何Integer $ s $ s $ smimate $ smimpter $ simpty thy pemimpate $ smimptime ette umpta $ \ textUp {ex}（n，k_ {s，t}'）=ω（n^{\ frac {3} {2} {2} - \ frac {1} {2S}}}）$。在本文中，我们考虑了$ s = 3 $的情况。更准确地说，我们提供了一个明确的结构给予\ begin {align*} \ text {ex}（n，k_ {3,30}'）=ω（n^{\ frac {\ frac {4} {3}}}} {3}}），\ end end {align*}，从而减少了$ 10^$ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ 30 $。该结构是代数，它基于有限场上的某些方程式。
For a graph $H$, the 1-subdivision of $H$, denoted by $H'$, is the graph obtained by replacing the edges of $H$ by internally disjoint paths of length 2. Recently, Conlon, Janzer and Lee (arXiv: 1903.10631) asked the following question: For any integer $s\ge2$, estimate the smallest $t$ such that $\textup{ex}(n,K_{s,t}')=Ω(n^{\frac{3}{2}-\frac{1}{2s}})$. In this paper, we consider the case $s=3$. More precisely, we provide an explicit construction giving \begin{align*} \text{ex}(n,K_{3,30}')=Ω(n^{\frac{4}{3}}), \end{align*} which reduces the estimation for the smallest value of $t$ from a magnitude of $10^{56}$ to the number $30$. The construction is algebraic, which is based on some equations over finite fields.
