A new approach to solving three combinatorial enumeration problems on planar graphs

Charles J. Colbourn, J. Scott Provan, Dirk Vertigan

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

The purpose of this paper is to show how the technique of delta-wye graph reduction provides an alternative method for solving three enumerative function evaluation problems on planar graphs. In particular, it is shown how to compute the number of spanning trees and perfect matchings, and how to evaluate energy in the Ising "spin glass" model of statistical mechanics. These alternative algorithms require O(n2) arithmetic operations on an n-vertex planar grapha, and are relatively easy to implement.

Original languageEnglish (US)
Pages (from-to)119-129
Number of pages11
JournalDiscrete Applied Mathematics
Volume60
Issue number1-3
DOIs
StatePublished - Jun 23 1995
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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