On two Hamilton cycle problems in random graphs
β Scribed by Alan Frieze; Michael Krivelevich
- Book ID
- 107529090
- Publisher
- The Hebrew University Magnes Press
- Year
- 2008
- Tongue
- English
- Weight
- 155 KB
- Volume
- 166
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge-length. For fixed k β₯ 1, we prove that the first edge in the process that creates a k-connected graph coincides a.a.s. with
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.