The Ramsey number $r(G)$ of a graph $G$ is the minimum number $N$ such that any red-blue colouring of the edges of $K_N$ contains a monochromatic copy of $G$. Pavez-Signé, Piga and Sanhueza-Matamala proved that for any function $n\leq f(n) \leq r(K_n)$, there is a sequence of connected graphs $(G_n)_{n\in \mathbb{N}}$ with $|V(G_n)|=n$ such that $r(G_n)=\Theta(f(n))$ and conjectured that $G_n$ can additionally have arbitrarily large connectivity. In this note we prove their conjecture.
@article{10_37236_12547,
author = {Isabel Ahme and Alexander Scott},
title = {Graphs with arbitrary {Ramsey} number and connectivity},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/12547},
zbl = {1556.05095},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12547/}
}
TY - JOUR
AU - Isabel Ahme
AU - Alexander Scott
TI - Graphs with arbitrary Ramsey number and connectivity
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12547/
DO - 10.37236/12547
ID - 10_37236_12547
ER -
%0 Journal Article
%A Isabel Ahme
%A Alexander Scott
%T Graphs with arbitrary Ramsey number and connectivity
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12547/
%R 10.37236/12547
%F 10_37236_12547
Isabel Ahme; Alexander Scott. Graphs with arbitrary Ramsey number and connectivity. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12547
