A fan Fn is a graph consisting of n triangles, all having precisely one common vertex. Currently, the best known bounds for the Ramsey number R(Fn) are 9n/2−5≤R(Fn)≤11n/2+6, obtained by Chen, Yu and Zhao. We improve the upper bound to 31n/6+O(1).
@article{arxiv.2109.07935,
title = {A New Upper Bound for the Ramsey Number of Fans},
author = {Vojtěch Dvořák and Harry Metrebian},
journal= {arXiv preprint arXiv:2109.07935},
year = {2021}
}