### 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 G^{n} is a random graph with 1 2nlogn+ 1 2nlogn+f(n)n edges and f(n>)→∞, then G^{n} is Hamiltonian, with probability tending to 1. We shall prove that if a graph G^{n} has n vertices and 1 2nlogn+ 1 2nlogn+cn edges, then it is Hamiltonian with probability P_{c} tending to exp exp(-2c) as n→∞.

Original language | English (US) |
---|---|

Pages (from-to) | 55-63 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 43 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1983 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics*,

*43*(1), 55-63. https://doi.org/10.1016/0012-365X(83)90021-3

}

*Discrete Mathematics*, vol. 43, no. 1, pp. 55-63. https://doi.org/10.1016/0012-365X(83)90021-3

**Limit distribution for the existence of hamiltonian cycles in a random graph.** / Komlos, Janos; Szemerédi, Endre.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Komlos, Janos

AU - Szemerédi, Endre

PY - 1983/1/1

Y1 - 1983/1/1

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→∞.

UR - http://www.scopus.com/inward/record.url?scp=0037606981&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037606981&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(83)90021-3

DO - 10.1016/0012-365X(83)90021-3

M3 - Article

AN - SCOPUS:0037606981

VL - 43

SP - 55

EP - 63

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -