Sums, products and ratios along the edges of a graph
Combinatorics
2018-02-20 v1 Number Theory
Abstract
In their seminal paper Erd\H{o}s and Szemer\'edi formulated conjectures on the size of sumset and product set of integers. The strongest form of their conjecture is about sums and products along the edges of a graph. In this paper we show that this strong form of the Erd\H{o}s-Szemer\'edi conjecture does not hold. We give upper and lower bounds on the cardinalities of sumsets, product sets and ratio sets along the edges of graphs.
Cite
@article{arxiv.1802.06405,
title = {Sums, products and ratios along the edges of a graph},
author = {Noga Alon and Imre Ruzsa and Jozsef Solymosi},
journal= {arXiv preprint arXiv:1802.06405},
year = {2018}
}