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arXiv · 0709.2322

Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions

Jesper Lykke Jacobsen
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Abstract

We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest.

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BibTeXRIS

Jesper Lykke Jacobsen. 2007-09-14. Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions. https://doi.org/10.1088/1751-8113/40/49/003

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