Structure and Recognition of Graphs with No 6-wheel Subdivision

The subgraph homeomorphism problem has been shown by Robertson and Seymour to be polynomial-time solvable for any fixed pattern graph H. The result, however, is not practical, involving constants that are worse than exponential in |H|. Practical algorithms have only been developed for a few specific pattern graphs, the most recent of these being the wheels with four and five spokes. This paper looks at the subgraph homeomorphism problem where the pattern graph is a wheel with six spokes. The main result is a theorem characterizing graphs that do not contain subdivisions of W ₆. We give an efficient algorithm for solving the subgraph homeomorphism problem for W ₆. We also give a strengthening of the previous W ₅ result.