On the Ramsey number of the double star

Freddy Flores Dubó; Maya Stein

paper

On the Ramsey number of the double star

arXiv:2401.01274

Abstract

The double star $S (m_{1}, m_{2})$ is obtained from joining the centres of a star with $m_{1}$ leaves and a star with $m_{2}$ leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of $S (m_{1}, m_{2})$ , for positive $m_{1}, m_{2}$ fulfilling $(5 + 1) m_{2} /2 < m_{1} < 3 m_{2}$ . Our result implies that for all positive $m$ , the Ramsey number of the double star $S (2 m, m)$ is at most $4.275 m$ .