Published online by Cambridge University Press: 13 May 2015
For two given graphs $G_{1}$ and
$G_{2}$, the Ramsey number
$R(G_{1},G_{2})$ is the smallest integer
$N$ such that, for any graph
$G$ of order
$N$, either
$G$ contains
$G_{1}$ as a subgraph or the complement of
$G$ contains
$G_{2}$ as a subgraph. A fan
$F_{l}$ is
$l$ triangles sharing exactly one vertex. In this note, it is shown that
$R(F_{n},F_{m})=4n+1$ for
$n\geq \max \{m^{2}-m/2,11m/2-4\}$.