On planar regular graphs degree three without Hamiltonian cycles

TL;DR

This paper explores the conditions under which planar regular graphs of degree three lack Hamiltonian cycles, providing necessary conditions and constructing specific examples of such graphs.

Contribution

It introduces a necessary condition for the existence of Hamiltonian cycles in these graphs and constructs explicit examples without such cycles.

Findings

Identified a necessary condition for Hamiltonian cycles in planar degree-three graphs.

Constructed explicit examples of planar regular graphs of degree three without Hamiltonian cycles.

Abstract

Necessary condition to have Hamiltonian cycle in planar graph is given. Examples of regular planar graphs degree three without Hamiltonian cycle are built.