Cubic planar Hamiltonian graphs of various types

Abstract

Let U be the set of cubic planar hamiltonian graphs, A the set of graphs G in U such that G - upsilon is hantiltonian for any vertex upsilon of G, B the set of graphs G in U such that G - e 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 A, B, 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. (c) 2006 Elsevier B.V. All rights reserved.