Hamilton Cycles in Random Graphs with a Fixed Degree Sequence
β Scribed by Cooper, Colin; Frieze, Alan; Krivelevich, Michael
- Book ID
- 118197777
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2010
- Tongue
- English
- Weight
- 212 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0895-4801
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G n,m,k denote the space of simple graphs with n vertices, m edges, and minimum degree at least k, each graph G being equiprobable. Let G have property A k , if G contains (k -1)/2 edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size n/2 . We prove that, for
Let a random graph G be constructed by adding random edges one by one, starting with n isolated vertices. We show that with probability going to one as n goes to infinity, when G first has minimum degree two, it has at least (log n)('-')" distinct hamilton cycles for any fixed E > 0.