Hamiltonian Cycles on a Random Three-coordinate Lattice

Abstract

Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a function of v. Furthermore we express the partition function of the corresponding statistical model as an elliptic integral.

Comments: 10 pages, LaTeX, 3 eps-figures, one reference added