Counting Matchings in Graphs
β Scribed by E.J. Farrell
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 488 KB
- Volume
- 324
- Category
- Article
- ISSN
- 0016-0032
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β¦ Synopsis
A general formula is derivedfor the matching polynomial of an arbitrary graph G. This yields a methodfor counting matchings in graphs. From the general formula, explicit formulae are deducedfor the number of k-matchings in several well-known families of graphs.
π SIMILAR VOLUMES
## Abstract The matching polynomial Ξ±(__G, x__) of a graph __G__ is a form of the generating function for the number of sets of __k__ independent edges of __G__. in this paper we show that if __G__ is a graph with vertex __v__ then there is a tree __T__ with vertex __w__ such that \documentclass{ar
## Abstract In this paper, we show that the edge set of a cubic graph can always be partitioned into 10 subsets, each of which induces a matching in the graph. This result is a special case of a general conjecture made by ErdΓΆs and NeΕ‘etΕil: For each __d__ β₯ 3, the edge set of a graph of maximum de
## Abstract A graph __G__ is __collapsible__ if for every even subset __R__ β __V__(__G__), there is a spanning connected subgraph of __G__ whose set of odd degree vertices is __R__. A graph is __reduced__ if it does not have nontrivial collapsible subgraphs. Collapsible and reduced graphs are defi