Field theoretic approach to the counting problem of Hamiltonian cycles of graphs
- 1 July 1998
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 58 (1) , 128-132
- https://doi.org/10.1103/physreve.58.128
Abstract
A field theoretic representation of the number of Hamiltonian cycles of graphs is studied. By integrating out quadratic fluctuations around the saddle point, one obtains an estimate of a number which reflects characteristics of graphs well. The accuracy of the estimate is verified by applying it to two-dimensional square lattices with various boundary conditions. This is an example of how to extract meaningful information from the quadratic approximation of the field theory representation.Keywords
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