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.Comment: 10 pages, LaTeX, 3 eps-figures, one reference adde