Field theoretic approach to the counting problem of Hamiltonian cycles of graphs

Preprint

21 July 1998

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/9711152

Abstract

A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around the saddle point, one obtains an estimate for the number which reflects characteristics of graphs well. The accuracy of the estimate is verified by applying it to 2d square lattices with various boundary conditions. This is the first example of extracting meaningful information from the quadratic approximation to the field theory representation.

Keywords

HAMILTONIAN CYCLES
CYCLES OF GRAPHS
COUNTING PROBLEM
FIELD THEORETIC
REPRESENTATION
SADDLE POINT
GRAPHS WELL

All Related Versions

Version 1, 1997-11-17, ArXiv
Version 2, 1997-12-11, ArXiv
Version 3, 1998-04-08, ArXiv
Version 4, 1998-07-21, ArXiv
Published version: Physical Review E, 58 (1), 128.

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