论文标题
在Turán的数字上，$ 4 $ - 图
On Turán numbers of the complete $4$-graphs
论文作者
论文摘要
Turán数字$ t（n，α+1，r）$是$ n $ vertex $ r $ r $ graph的最小边数，其独立数不超过$α$。对于每个$ r \ geq 2 $，都存在$ t _*（r）$，这样$ t（n，α+1，r）= t _*（r）\：n^r \：α^{1-r} \：（1+o（1+o（1+o（1）$）as $α / r \ to $α / r \ to to \ to to \ to to \ n / r \ to \ in / r \ to \ n / r n / n / / n / n / / n / /α\ f infty。众所周知，$ t _*（2）= 1/2 $，$ t _*（3）$的猜想值为$ 2/3 $。我们证明$ t _*（4）<0.706335 \：$。
The Turán number $T(n,α+1,r)$ is the minimum number of edges in an $n$-vertex $r$-graph whose independence number does not exceed $α$. For each $r\geq 2$, there exists $t_*(r)$ such that $T(n,α+1,r) = t_*(r) \: n^r \: α^{1-r} \: (1+o(1))$ as $α/ r \to\infty$ and $n / α\to\infty$. It is known that $t_*(2) = 1/2$, and the conjectured value of $t_*(3)$ is $2/3$. We prove that $t_*(4) < 0.706335\:$.
