  For a given pair of two graphs $(F,H)$, let $R(F,H)$ be the smallest positive
integer $r$ such that for any graph $G$ of order $r$, either $G$ contains $F$
as a subgraph or the complement of $G$ contains $H$ as a subgraph. Baskoro,
Broersma and Surahmat (2005) conjectured that \[ R(F_\ell,K_n)=2\ell(n-1)+1 \]
for $\ell\ge n\ge3$, where $F_\ell$ is the join of $K_1$ and $\ell K_2$. In
this paper, we prove that this conjecture is true for the case $n=6$.
