  We present exact and heuristic algorithms that find, for a given family of
graphs, a graph that contains each member of the family as an induced subgraph.
For $0 \leq k \leq 6$, we give the minimum number of vertices $f(k)$ in a graph
containing all $k$-vertex graphs as induced subgraphs, and show that $16 \leq
f(7) \leq 18$. For $0 \leq k \leq 5$, we also give the counts of such graphs,
as generated by brute-force computer search. We give additional results for
small graphs containing all trees on $k$ vertices.
