On sums and products along the edges, II

TL;DR

This paper advances constructions related to sums and products along graph edges, building on prior work to address questions posed by Erdős and Szemerédi, and offers additional insights into related problems.

Contribution

It provides improved constructions for sums and products along graph edges and discusses related variations of the problem.

Findings

Enhanced constructions for sums and products along edges.

Addresses Erdős and Szemerédi's question with new methods.

Includes observations on related problem variants.

Abstract

This note is a continuation of an earlier paper by the authors. We describe improved constructions addressing a question of Erd\H{o}s and Szemer\'edi on sums and products of real numbers along the edges of a graph. We also add a few observations about related versions of the problem.