Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T07:14:39.625Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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