  We give a simple deterministic constant-round algorithm in the congested
clique model for reducing the number of edges in a graph to $n^{1+\varepsilon}$
while preserving the minimum spanning forest, where $\varepsilon > 0$ is any
constant. This implies that in the congested clique model, it is sufficient to
improve MST and other connectivity algorithms on graphs with slightly
superlinear number of edges to obtain a general improvement. As a byproduct, we
also obtain a simple alternative proof showing that MST can be computed
deterministically in $O(\log \log n)$ rounds.
