Topics in Combinatorics and Graph Theory || Counting Perfect Matchings in Lattice Graphs
β Scribed by Bodendiek, Rainer; Henn, Rudolf
- Book ID
- 120208380
- Publisher
- Physica-Verlag HD
- Year
- 1990
- Weight
- 587 KB
- Category
- Article
- ISBN
- 3642469086
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a plane bipartite graph which admits a perfect matching and with distinguished faces called holes. Let MG denote the perfect matchings graph: its vertices are the perfect matchings of G, two of them being joined by an edge, if and only if they di er only on an alternating cycle bounding a f
We give lower and upper bounds for the number of reducible ears as well as upper bounds for the number of perfect matchings in an elementary bipartite graph. An application to chemical graphs is also discussed. In addition, a method to construct all minimal elementary bipartite graphs is described.
Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given