A plane graph is called symmetric if it is invariant under the reflection across some straight line. We prove a result that expresses the number of perfect matchings of a large class of symmetric graphs in terms of the product of the number of matchings of two subgraphs. When the graph is also centr
Matching and symmetry of graphs
โ Scribed by Haruo Hosoya
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 809 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The matching graph M (G) of a graph G is that graph whose vertices are the maximum matchings in G and where two vertices M 1 and M 2 of M (G) this graph models a metric space whose metric is defined on the set of maximum matchings in G. Which graphs are matching graphs of some graph is not known in
## Abstract A graph __G__ is __collapsible__ if for every even subset __R__ โ __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
We say that a simple graph G is induced matching extendable, shortly IM-extendable, if every induced matching of G is included in a perfect matching of G. The main results of this paper are as follows: (1) For every connected IM-extendable graph 2 |V (G)| -2; the equality holds if and only if G โผ
Let G = ( Y E ) be an undirected graph. A subset F of E is a matching cutset of G if no two edges of Fare incident with the same point, and G-F has more components than G. ChGatal [2] proved that it is NP-complete to recognize graphs with a matching cutset even if the input is restricted to graphs w