  Given a graph $G$ and a positive integer $k$, define the \emph{Gallai-Ramsey
number} to be the minimum number of vertices $n$ such that any $k$-edge
coloring of $K_n$ contains either a rainbow (all different colored) triangle or
a monochromatic copy of $G$. In this paper, we obtain general upper and lower
bounds on the Gallai-Ramsey numbers for fans $F_{m} = K_{1} + mK_{2}$ and prove
the sharp result for $m = 2$ and for $m = 3$ with $k$ even.
