关于圈的归纳

摘要：

1975年，Pippenger和Golumbic证明了$n$顶点上的图至多存在$2e(n/k)^k$诱导的$k$ -圈。这个界比由爆破构造得到的简单下界大一个乘性因子$2e$。Pippenger和Golumbic指出后一个下界本质上是紧的。本文建立了$(128e/81) \cdot (n/k)^k$的一个较好的上界。这是证明上述猜想的第一个进展。

英文摘要：

In 1975 Pippenger and Golumbic proved that any graph on $n$ vertices admits at most $2e(n/k)^k$ induced $k$-cycles. This bound is larger by a multiplicative factor of $2e$ than the simple lower bound obtained by a blow-up construction. Pippenger and Golumbic conjectured that the latter lower bound is essentially tight. In the present paper we establish a better upper bound of $(128e/81) \cdot (n/k)^k$. This constitutes the first progress towards proving the aforementioned conjecture since it was posed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。