TY - JOUR
T1 - A new approach to solving three combinatorial enumeration problems on planar graphs
AU - Colbourn, Charles J.
AU - Provan, J. Scott
AU - Vertigan, Dirk
N1 - Funding Information:
Research of the first author is supported by NSERC Canada under grant number A0579. Research of the second author is partially supported by NSF Grant CCR-9200572; work performed while on leave at the University of Waterloo.
PY - 1995/6/23
Y1 - 1995/6/23
N2 - 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.
AB - 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.
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U2 - 10.1016/0166-218X(95)E0111-3
DO - 10.1016/0166-218X(95)E0111-3
M3 - Article
AN - SCOPUS:0037565829
SN - 0166-218X
VL - 60
SP - 119
EP - 129
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 1-3
ER -