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Kasteleyn's Theorem and Arbitrary Graphs

Published online by Cambridge University Press:  20 November 2018

Charles H. C. Little
Charles H. C. Little*
Affiliation:
University of Waterloo, Waterloo, Ontario
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Familiarity with the basic notions of graph theory is assumed. Loops and multiple edges are not permitted. An orientation of an edge e of a graph G is a designation of one of the ends of e as the positive end and the other as the negative end. We say that e is oriented from the positive end to the negative end. If e joins vertex v to vertex w and v is the positive end of e, we write e = (v, w). An orientation of G is a set of orientations, one for each edge of G; a graph with an orientation is called a directed graph.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 758 - 764
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Kasteleyn, P. W., Graph theory and crystal physics, in Harary, F., ed., Graph Theory and Theoretical Physics (Academic Press, London, 1967), pp. 43-110.Google Scholar
2. Cayley, A., Sur les déterminants gauches, Crelle's J. 88 (1847), 93–94.Google Scholar
3. Halton, J., A combinatorial proof of Cayley1 s theorem on Pfaffians, J. Combinatorial Theory 1 (1966), 224–232.Google Scholar
4. Pla, J.-M., Sur l’utilisation d'un Pfaffien dans l’étude des couplages parfaits d'un graphe, C.R. Acad. Sci. Paris Sér. A-B 260 (1965), 2967–2970.Google Scholar