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Counting Matchings in Graphs

✍ 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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✦ 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.


πŸ“œ SIMILAR VOLUMES


Matchings in polytopal graphs
✍ B. GrΓΌnbaum πŸ“‚ Article πŸ“… 1974 πŸ› John Wiley and Sons 🌐 English βš– 667 KB
Induced matchings in bipartite graphs
✍ R.J. Faudree; A. GyΓ‘rfas; R.H. Schelp; Zs. Tuza πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 454 KB
Matchings and walks in graphs
✍ C. D. Godsil πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 527 KB

## 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

Induced matchings in cubic graphs
✍ Peter HorΓ‘k; He Qing; William T. Trotter πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 527 KB

## 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‘etΕ™il: For each __d__ β‰₯ 3, the edge set of a graph of maximum de

Collapsible graphs and matchings
✍ Zhi-Hong Chen; Hong-Jian Lai πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 286 KB

## Abstract A graph __G__ is __collapsible__ if for every even subset __R__ βŠ† __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