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

✍ Scribed by János Komlós; Endre Szemerédi

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
874 KB
Volume
43
Category
Article
ISSN
0012-365X

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✦ Synopsis

P&a proved that a random graph with clt 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 *n log n + in log log n + f(n)n edges and f(n) --*m, then G" is Hamiltonian, with probability tending to 1. We shall prove that if a graph G" has n vertices and $n log n + in log log n + cn edges, then it is Hamiltonian with probability PC tending to exp exp(-2) as n -+ 00. 0.1. In his paper [l] Lajos P&a proves that a random graph with n vertices and f(n) = cn log n edges contains a Hamiltonian cycle with a probability approaching 1 (as n 300).

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