The multipartite Ramsey number for the 3-path of length three

TL;DR

This paper investigates the multipartite Ramsey number for a specific 3-path graph with multiple colors, establishing an upper bound that improves understanding of its growth rate.

Contribution

The paper provides a new upper bound on the multipartite Ramsey number for the 3-path of length three with n colors, including an explicit constant.

Findings

Established an upper bound of R(P^3_3;n) ≤ 1.97466... n + 7√n

Improved understanding of the growth rate of multipartite Ramsey numbers for specific graphs

Explicit constant provided for the upper bound

Abstract

We study the Ramsey number for the 3-path of length three and $n$ colors and show that $R(P^3_3;n)\le \lambda_0 n+7\sqrt{n}$, for some explicit constant $\lambda_0=1.97466\dots$.