Counting Hamiltonian cycles on planar random lattices

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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

Scientific paper

10.1142/S0217732398000784

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.

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