On conjectures and problems of Ruzsa concerning difference graphs of S-units
Number Theory
2014-09-09 v1
Abstract
Given a finite nonempty set of primes S, we build a graph with vertex set 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 , and also a problem of Ruzsa concerning the existence of subgraphs of which are not induced subgraphs.
Keywords
Cite
@article{arxiv.1409.2218,
title = {On conjectures and problems of Ruzsa concerning difference graphs of S-units},
author = {Ante Custic and Lajos Hajdu and Dijana Kreso and Robert Tijdeman},
journal= {arXiv preprint arXiv:1409.2218},
year = {2014}
}
Comments
15 pages