  The triangle removal lemma states that a simple graph with o(n^3) triangles
can be made triangle-free by removing o(n^2) edges. It is natural to ask if
this widely used result can be extended to multi-graphs (or equivalently,
weighted graphs). In this short paper we rule out the possibility of such an
extension by showing that there are multi-graphs with only n^{2+o(1)} triangles
that are still far from being triangle-free. On the other hand, we show that
for some g(n)=\omega(1), if a multi-graph (or weighted graph) has only g(n)n^2
triangles then it must be close to being triangle-free. The proof relies on
variants of the Ruzsa-Szemer\'edi theorem.
