Let q\*(G) denote the minimum integer t for which E(G) can be partitioned into t induced matchings of G. Faudree et al. conjectured that q\*(G)<d2, if G is a bipartite graph and d is the maximum degree of G. In this note, we give an affirmative answer for d=3, the first nontrivial case of this conje
On Matchings in Groups
โ Scribed by Jozsef Losonczy
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 125 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0196-8858
No coin nor oath required. For personal study only.
โฆ Synopsis
A matching property conceived for lattices is examined in the context of an arbitrary Abelian group. The Dyson e-transform and the CauchyแDavenport inequality from additive number theory are used to establish the existence of matchings.
๐ SIMILAR VOLUMES
where the class โฌ-GRAPHS is the set of graphs of maximum degree at most โฌ . แฎ 1997 John ## ลฝ .
We generalize Kasteleyn's method of enumerating the perfect matchings in a planar graph to graphs embedding on an arbitrary compact boundaryless 2-manifold S. Kasteleyn stated that perfect matchings in a graph embedding on a surface of genus g could be enumerated as a linear combination of 4 g Pfaff
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.