Nonhamiltonian 3-Connected Cubic Planar Graphs

Abstract

We establish that every cyclically 4-connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp, and we present all nonhamiltonian examples of order 42. In addition we list all nonhamiltonian cyclically 5-connected cubic planar graphs of order at most 52 and all nonhamiltonian 3-connected cubic planar graphs of girth 5 on at most 46 vertices. The fact that all 3-connected cubic planar graphs on at most 176 vertices and with face size at most 6 are hamiltonian is also verified.