HAMILTONIAN CYCLES ON A RANDOM 3-COORDINATE LATTICE

Consider a random three-coordinate lattice of spherical topology havin g 2v vertices and being densely covered by a single closed, self-avoid ing walk, i.e. being equipped with a Hamiltonian cycle. We determine t he number of such objects as a function of v. Furthermore, we express the partition function of the corresponding statistical model as an el liptic integral. (C) 1998 Elsevier Science B.V.