Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions
Statistical Mechanics
2009-11-13 v1
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.
Keywords
Cite
@article{arxiv.0709.2322,
title = {Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions},
author = {Jesper Lykke Jacobsen},
journal= {arXiv preprint arXiv:0709.2322},
year = {2009}
}