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The subgraph homeomorphism problem, where the pattern graph is a wheel with four or five spokes, is studied. The most important result is that any 34n~ected graph satisfying a simple edge co~eetivity condition has a W$homeomorph ilf it has a vertex v of degree at least 5 and a circuit, disjoint from v, of length at least 5. Efficient algorithms are describ& for these cases of the subgraph homeomorphism problem.doi:10.1016/0012-365x(88)90066-0 fatcat:b553jkcdsvhsfepc244gxavzha