  We find the minimal number of links in an embedding of any complete
$k$-partite graph on 7 vertices (including $K_7$, which has at least 21 links).
We give either exact values or upper and lower bounds for the minimal number of
links for all complete $k$-partite graphs on 8 vertices. We also look at larger
complete bipartite graphs, and state a conjecture relating minimal linking
embeddings with minimal book embeddings.
