# Limit distribution for the existence of hamiltonian cycles in a random graph

Janos Komlos, Endre Szemerédi

Research output: Contribution to journalArticle

136 Citations (Scopus)

### 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 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→∞.

Original language English (US) 55-63 9 Discrete Mathematics 43 1 https://doi.org/10.1016/0012-365X(83)90021-3 Published - Jan 1 1983 Yes

### Fingerprint

Hamiltonians
Hamiltonian circuit
Limit Distribution
Random Graphs
Graph in graph theory

### All Science Journal Classification (ASJC) codes

• Theoretical Computer Science
• Discrete Mathematics and Combinatorics

### Cite this

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title = "Limit distribution for the existence of hamiltonian cycles in a random graph",
abstract = "P{\'o}sa 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→∞.",
author = "Janos Komlos and Endre Szemer{\'e}di",
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In: Discrete Mathematics, Vol. 43, No. 1, 01.01.1983, p. 55-63.

Research output: Contribution to journalArticle

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T1 - Limit distribution for the existence of hamiltonian cycles in a random graph

AU - Komlos, Janos

AU - Szemerédi, Endre

PY - 1983/1/1

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N2 - 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→∞.

AB - 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→∞.

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