  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.

Statistical Mechanics;High Energy Physics - Lattice;High Energy Physics - Theory