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An effective algorithm for the enumeration of edge colorings and Hamiltonian cycles in cubic graphs

V. Ejov·N. Pugacheva·S. Rossomakhine·P. Zograf
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Abstract

We propose an effective algorithm that enumerates (and actually finds) all 3-edge colorings and Hamiltonian cycles in a cubic graph. The idea is to make a preliminary run that separates the vertices into two types: ``rigid'' (such that the edges incident to them admit a unique coloring) and ``soft'' ones (such that the edges incident to them admit two distinct colorings), and then to perform the coloring. The computational complexity of this algorithm is on a par with (or even below) the fastest known algorithms that find a single 3-edge coloring or a Hamiltonian cycle for a cubic graph.

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V. Ejov, N. Pugacheva, S. Rossomakhine, P. Zograf. 2006-10-26. An effective algorithm for the enumeration of edge colorings and Hamiltonian cycles in cubic graphs. https://arxiv.org/abs/math/0610779

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