2023/11/03 by Ahme, Isabel, Scott, Alex
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.01887
The Ramsey number r(G) of a graph G is the minimum number N such that any red-blue colouring of the edges of KN contains a monochromatic copy of G. Pavez-Signé, Piga and Sanhueza-Matamala proved that for any function n≤ f(n) ≤ r(Kn), there is a sequence of connected graphs (Gn)n∈ ℕ with |V(Gn)|=n such that r(Gn)=Θ(f(n)) and conjectured that Gn can additionally have arbitrarily large connectivity. In this note we prove their conjecture.