English

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

Combinatorics 2009-09-29 v1

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.

Keywords

Cite

@article{arxiv.math/0610779,
  title  = {An effective algorithm for the enumeration of edge colorings and Hamiltonian cycles in cubic graphs},
  author = {V. Ejov and N. Pugacheva and S. Rossomakhine and P. Zograf},
  journal= {arXiv preprint arXiv:math/0610779},
  year   = {2009}
}

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