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 languageEnglish (US)
Pages (from-to)55-63
Number of pages9
JournalDiscrete Mathematics
Volume43
Issue number1
DOIs
StatePublished - Jan 1 1983
Externally publishedYes

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

In: Discrete Mathematics, Vol. 43, No. 1, 01.01.1983, p. 55-63.

Research output: Contribution to journalArticle

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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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