  Practical algorithms for solving the Subgraph Homeomorphism Problem are known
for only a few small pattern graphs: among these are the wheel graphs with
four, five, six, and seven spokes. The length and difficulty of the proofs
leading to these algorithms increase greatly as the size of the pattern graph
increases. Proving a result for the wheel with six spokes requires extensive
case analysis on many small graphs, and even more such analysis is needed for
the wheel with seven spokes. This paper describes algorithms and programs used
to automate the generation and testing of the graphs that arise as cases in
these proofs. The main algorithm given may be useful in a more general context,
for developing other characterizations of SHP-related properties.
