Entropy bounds for perfect matchings and Hamiltonian cycles
β Scribed by Bill Cuckler; Jeff Kahn
- Publisher
- Springer-Verlag
- Year
- 2009
- Tongue
- English
- Weight
- 432 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let H be a set of connected graphs. A graph is said to be H-free if it does not contain any member of H as an induced subgraph. Plummer and Saito [J Graph Theory 50 (2005), 1-12] and Fujita et al. [J Combin Theory Ser B 96 (2006), 315-324] characterized all H with |H| β€ 2 such that every connected H
Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set
Let H be a k + 1 -uniform, D-regular hypergraph on n vertices and let H be the minimum number of vertices left uncovered by a matching in H. C j H , the j-codegree of H, is the maximum number of edges sharing a set of j vertices in common. We prove a general upper bound on H , based on the codegree