  We address the problem of computing a single linkage dendrogram. A possible
approach is to: (i) Form an edge weighted graph $G$ over the data, with edge
weights reflecting dissimilarities. (ii) Calculate the MST $T$ of $G$. (iii)
Break the longest edge of $T$ thereby splitting it into subtrees $T_L$, $T_R$.
(iv) Apply the splitting process recursively to the subtrees. This approach has
the attractive feature that Prim's algorithm for MST construction calculates
distances as needed, and hence there is no need to ever store the inter-point
distance matrix. The recursive partitioning algorithm requires us to determine
the vertices (and edges) of $T_L$ and $T_R$. We show how this can be done
easily and efficiently using information generated by Prim's algorithm without
any additional computational cost.
