  Increasingly, biologists are constructing evolutionary trees on large numbers
of overlapping sets of taxa, and then combining them into a `supertree' that
classifies all the taxa. In this paper, we ask how much coverage of the total
set of taxa is required by these subsets in order to ensure we have enough
information to reconstruct the supertree uniquely. We describe two results - a
combinatorial characterization of the covering subsets to ensure that at most
one supertree can be constructed from the smaller trees (whatever trees these
may be) and a more liberal analysis that asks only that the supertree is highly
likely to be uniquely specified by the tree structure on the covering subsets.
