Simple numerical algorithm for generating Hamiltonian cycles and edge labels on planar cubic maps

TL;DR

This paper introduces a simple numerical algorithm for constructing Hamiltonian cycles and edge labels in planar cubic maps, supported by theoretical and numerical validation, including a Python implementation.

Contribution

The paper presents a novel, straightforward algorithm for generating Hamiltonian cycles and edge labels in cubic planar maps, with a publicly available Python implementation.

Findings

Algorithm successfully constructs Hamiltonian cycles in cubic planar maps.

Theoretical support aligns with the Four Colour Theorem.

Python implementation demonstrates practical applicability.

Abstract

In this work we present an algorithm with which any arbitrary cubic planar map may be constructed through successive edge insertion while simultaneously constructing a set of proper edge labels and Hamiltonian cycles for each configuration. We present a publicly available Python implementation of this algorithm, and discuss both theoretical and numerical support for its validity, with reference to the well-known Four Colour Theorem.