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Operations preserving the pfaffian property of a graph

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

C. H. C. Little  and
F. Rendl
C. H. C. Little
Affiliation:
Massey UniversityPalmerston NorthNew Zealand.
F. Rendl
Affiliation:
Technische Universität GrazKopernikusgasse 24 A-8010 Graz, Austria
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Abstract

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Pfaffian graphs are those which can be oriented so that the 1-factors have equal sign, as calculated according to the prescription of Kasteleyn. We consider various operations on graphs and examine their effect on the Pfaffian property. We show that the study of Pfaffian graphs may be reduced to the case of subcubic graphs (graphs in which no vertex has degree greater than 3) or bricks (3-connected bicritical graphs).

MSC classification

Secondary: 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 2 , April 1991 , pp. 248 - 257
Copyright
Copyright © Australian Mathematical Society 1991

References

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