  We show that any one-round algorithm that computes a minimum spanning tree
(MST) in the unicast congested clique must use a link bandwidth of
$\Omega(\log^3 n)$ bits in the worst case. Consequently, computing an MST under
the standard assumption of $O(\log n)$-size messages requires at least $2$
rounds. This is the first round complexity lower bound in the unicast congested
clique for a problem where the output size is small, i.e., $O(n\log n)$ bits.
Our lower bound holds as long as every edge of the MST is output by an incident
node. To the best of our knowledge, all prior lower bounds for the unicast
congested clique either considered problems with large output sizes (e.g.,
triangle enumeration) or required every node to learn the entire output.
