Pósa proved that a random graph with cn log n edges is Hamiltonian with probability tending to 1 if c > 3. Korsunov improved this by showing that, if Gn is a random graph with 1 2nlogn+ 1 2nlogn+f(n)n edges and f(n>)→∞, then Gn is Hamiltonian, with probability tending to 1. We shall prove that if a graph Gn has n vertices and 1 2nlogn+ 1 2nlogn+cn edges, then it is Hamiltonian with probability Pc tending to exp exp(-2c) as n→∞.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics