Cubic planar hamiltonian graphs of various types Original Research Article

Let U be the set of cubic planar hamiltonian graphs, A the set of graphs G in U such that image is hamiltonian for any vertex image of G, B the set of graphs G in U such that image is hamiltonian for any edge e of G, and C the set of graphs G in U such that there is a hamiltonian path between any two different vertices of G. With the inclusion and/or exclusion of the sets image, and C, U is divided into eight subsets. In this paper, we prove that there is an infinite number of graphs in each of the eight subsets.