论文标题
两个附近的理性指数
Rational exponents near two
论文作者
论文摘要
长期以来的Erds和Simonovits的猜想指出，对于每一个合理的$ r $，$ 1 $至2 $之间都有一个图$ h $，因此$ n $ vertices上$ h $ fertices in $ n $ dertices中最大的边缘为$θ（n^r）$。在回答江，江和马的提出的一个问题时，我们表明，该猜想对表格的所有理性$ 2- a/b $的所有理性都持有$ a $，而$ a $则足够大。
A longstanding conjecture of Erdős and Simonovits states that for every rational $r$ between $1$ and $2$ there is a graph $H$ such that the largest number of edges in an $H$-free graph on $n$ vertices is $Θ(n^r)$. Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form $2 - a/b$ with $b$ sufficiently large in terms of $a$.
