Neighborhood conditions and edge-disjoint perfect matchings, Discrete Mathematics 91 (1991) 33-43. A graph G satisfies the neighborhood condition ANC(G) 2 m if, for all pairs of vertices of G, the union of their neighborhoods has at least m vertices. For a fixed positive integer k, let G be a graph
Disjoint matchings of graphs
β Scribed by Kenneth Lebensold
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 250 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## 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
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.
A graph with at least two vertices is matching covered if it is connected and each edge lies in some perfect matching. A matching covered graph G is extremal if the number of perfect matchings of G is equal to the dimension of the lattice spanned by the set of incidence