Abstract

The double star S(m1,m2) is obtained from joining the centres of a star with m1 leaves and a star with m2≤m1 leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of S(m1,m2) which holds for all m1,m2 with [Formula presented]. Our result implies that for all positive m, the Ramsey number of the double star S(2m,m) is at most ⌈4.275m⌉+1. © 2024 Elsevier B.V.