@article{9a3a4028864e41c8ab7b630ae733b53b,
title = "Sums, products, and ratios along the edges of a graph",
abstract = "In their seminal paper Erdos and Szemer{\'e}di 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 Erdos–Szemer{\'e}di 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.",
keywords = "Incidence geometry, Sum-product problems, Sumset",
author = "Noga Alon and Imre Ruzsa and J{\'o}zsef Solymosi",
note = "Publisher Copyright: {\textcopyright} 2020 Universitat Autonoma de Barcelona. All rights reserved.",
year = "2020",
doi = "10.5565/PUBLMAT6412006",
language = "אנגלית",
volume = "64",
pages = "143--155",
journal = "Publicacions Matematiques",
issn = "0214-1493",
publisher = "Universitat Autonoma de Barcelona",
number = "1",
}