确定图类速度的快速方法
Determining Factorial Speed Fast
AI总结：
本文证明了有限二进制语言可表示的图类具有阶乘速度，并将部分之前未知速度的图类归类为阶乘，同时证明k-字母图具有指数速度。
摘要：
图类的速度衡量的是在n个顶点上能找到多少个标记图属于该类。这个图类复杂度函数在graphclasses.org上明确给出。然而，对于许多图类，其速度状态被分类为未知。在本文中，我们证明了任何可以用有限二进制语言表示的图类速度最多为阶乘，即其速度函数行为类似于2^{Θ(n log n)}，并利用这一标准将许多之前速度未知的图类分类为阶乘。作为结果，几个图类之间的包含关系现在可以被看作是严格的。我们还证明k-字母图具有指数速度，即速度函数位于2^{Θ(n)}内。
英文摘要：
The speed of a graph class $\cal G$ measures how many labeled graphs on $n$ vertices one can find in $\cal G$. This graph class complexity function is explicitly provided on graphclasses.org. However, for many graph classes, their speed status is classified as \emph{unknown}. In this paper, w}\shortversion{W}e show that any graph class representable by a finite binary language has at most factorial speed, meaning that its speed function behaves like $2^{Θ(n\log n)}$, and we use this criterion to classify many graph classes whose speed was previously unknown as factorial. As a consequence, inclusions between several graph classes can now be seen to be proper. We also prove that $k$-letter graphs have exponential speed, i.e., the speed function lies in $2^{Θ(n)}$.
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。
