Limit distribution for the existence of Hamiltonian cycles in a random graph

1Citations
Citations of this article
10Readers
Mendeley users who have this article in their library.

Abstract

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 frac(1, 2) n log n + frac(1, 2) n log log n + 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 frac(1, 2) n log n + frac(1, 2) n log log n + cn edges, then it is Hamiltonian with probability Pc tending to exp exp (- 2 c) as n → ∞. © 1983.

Cite

CITATION STYLE

APA

Komlós, J., & Szemerédi, E. (2006). Limit distribution for the existence of Hamiltonian cycles in a random graph. Discrete Mathematics, 306(10–11), 1032–1038. https://doi.org/10.1016/j.disc.2006.03.022

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free