Counting Hamiltonian cycles on planar random lattices

Abstract

A Hamiltonian cycle of a graph is a closed path which visits each of the vertices once and only once. In this article, Hamiltonian cycles on planar random lattices are considered. The generating function for the number of Hamiltonian cycles is obtained and its singularity is studied. Relation to two-dimensional quantum gravity is discussed.

Comments: 8 pages, 3 figures, uses latex2e and graphicx, typos corrected and a reference added. Presentation improved