Pohl-Warnsdorf – Revisited

Two new series of graphs are introduced. Properties of these graphs make them suitable as test beds for Hamiltonian path heuristics. The graphs are planar and regular of degree 3, and each series has a simple recursive definition. These graphs are “conceptual adversaries” to methods that try to exploit local characteristics. For each series, we give an analysis showing that the number of Hamiltonian paths in these graphs grows polynomially in the number of nodes of the graph. For both series, the analysis gives the degree of the polynomial. For one of the series, the number of Hamiltonian paths is determined exactly. A companion paper (LaFall and Pohl 2004) gives experimental results from applying the Pohl-Warnsdorf heuristic to these graphs.