Hamiltonian Cycles on a Random Three-coordinate Lattice
  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. 
B. Eynard (Durham), E. Guitter (Saclay) and C. Kristjansen (NBI)