Edge number report 1: State of the art estimates for $n \leq 43$

TL;DR

This paper compiles known bounds for e-numbers up to n=43, providing a comprehensive report on their current estimates and some implications for classical Ramsey numbers, with minimal proofs included.

Contribution

It offers the first detailed compilation of bounds for e-numbers up to n=43, summarizing known results and highlighting gaps in the proofs.

Findings

Most e-number bounds for n ≤ 43 are known, with only 24 remaining unknown.

The report includes bounds for all lower and upper e-number estimates within the range.

Some implications for classical Ramsey number bounds are discussed.

Abstract

This first extracted report contains all lower and upper bounds for e-numbers $e(3,k;n)$, for $n \leq 43$, that I know. All but 24 of them are known (exactly).Very little of the proofs is given. A few consequences for upper classical Ramsey number bounds are mentioned.