On the independence number and Hamiltonicity of uniform random intersection graphs
β Scribed by S. Nikoletseas; C. Raptopoulos; P.G. Spirakis
- Book ID
- 113927540
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 295 KB
- Volume
- 412
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let (Y(G~,~) denote the independence number of the random graph Gn,p. Let d = np. We show that if E > 0 is fixed then with probability going to 1 as n + m cu(G& -$t (log d -log log dlog 2 + 1) < 7 provided d, s d = o(n), where d, is some fixed constant.
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.