Hamiltonian cycles on random lattices of arbitrary genus
Statistical Mechanics
2007-05-23 v5 Soft Condensed Matter
High Energy Physics - Lattice
High Energy Physics - Theory
Abstract
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It has been difficult to count the number of Hamiltonian cycles on regular lattices with periodic boundary conditions, e.g. lattices on a torus, due to the presence of winding modes. In this paper, the exact number of Hamiltonian cycles on a random trivalent fat graph drawn faithfully on a torus is obtained. This result is further extended to the case of random graphs drawn on surfaces of an arbitrary genus. The conformational exponent gamma is found to depend on the genus linearly.
Cite
@article{arxiv.cond-mat/9806349,
title = {Hamiltonian cycles on random lattices of arbitrary genus},
author = {Saburo Higuchi},
journal= {arXiv preprint arXiv:cond-mat/9806349},
year = {2007}
}
Comments
16 pages, 4 figures, latex2e, uses graphicx and amsfonts. minor corrections