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

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