We generalize Kasteleyn's method of enumerating the perfect matchings in a planar graph to graphs embedding on an arbitrary compact boundaryless 2-manifold S. Kasteleyn stated that perfect matchings in a graph embedding on a surface of genus g could be enumerated as a linear combination of 4 g Pfaff
β¦ LIBER β¦
Dimers on Graphs in Non-Orientable Surfaces
β Scribed by David Cimasoni
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 471 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0377-9017
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## Abstract In this article, we apply a cutting theorem of Thomassen to show that there is a function __f__: N β N such that if __G__ is a 3βconnected graph on __n__ vertices which can be embedded in the orientable surface of genus __g__ with faceβwidth at least __f__(__g__), then __G__ contains a
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