关于S-单位差图的Ruzsa定理和问题
On conjectures and problems of Ruzsa concerning difference graphs of S-units
摘要：
给定一个有限的非空素数集S，如果x-y的分子和分母的素除子都来自S，则通过连接x和y建立一个顶点集为$\mathbb{Q}$的图$\mathcal{G}$.本文解决了Ruzsa提出的关于$\mathcal{G}$的诱导非退化圈的可能大小的两个问题，以及Ruzsa提出的关于$\mathcal{G}$的非诱导子图的子图的存在性问题.
英文摘要：
Given a finite nonempty set of primes S, we build a graph $\mathcal{G}$ with vertex set $\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\mathcal{G}$ which are not induced subgraphs.
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。
