Beyond Grinberg Equation in Cubic Planar Graphs

Abstract

In this paper, Grinberg equation related to the Hamiltonicity of cubic planar graphs is revisited using the cycle base description of the graph and the related Laplacian. The advantages and the limitations of a pure Algebraic approach to Hamiltonicity are shown. Examples, showing the limitations are presented, too. Further possible approaches are suggested. Some unexpected results are shown, too.

Keywords

• Planar graphs
• Hamiltonicity
• Cycles Base
• Grinberg equation
• Laplacian
• Hamiltonian cycle