论文标题
在六角形的爆炸数量上
On the Turán number of the blow-up of the hexagon
论文作者
论文摘要
图$ f $的$ r $ blowup，用$ f [r] $表示，是通过用独立尺寸$ r $的独立集和$ k_ {r，r，r} $的独立套件替换$ f $的顶点和边缘获得的图表。对于双方图$ f $，关于$ f [r] $的Turán数量的数量级知之甚少。在本文中，我们证明了$ \ mathrm {ex}（n，c_6 [2]）= o（n^{5/3}）$，更一般而言，对于任何积极的整数$ t $，$ \ mathrm {exrm {ex}（n，θ_{n，θ__{3，t} [3，t} [2] [2] [2] [2] [2] [2] = o（n^^{5/3}）$。当$ t $足够大时，这很紧。
The $r$-blowup of a graph $F$, denoted by $F[r]$, is the graph obtained by replacing the vertices and edges of $F$ with independent sets of size $r$ and copies of $K_{r,r}$, respectively. For bipartite graphs $F$, very little is known about the order of magnitude of the Turán number of $F[r]$. In this paper we prove that $\mathrm{ex}(n,C_6[2])=O(n^{5/3})$ and, more generally, for any positive integer $t$, $\mathrm{ex}(n,θ_{3,t}[2])=O(n^{5/3})$. This is tight when $t$ is sufficiently large.
