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

Search strategies for developing characterizations of graphs without small wheel subdivisions