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Hamiltonian cycles on random lattices of arbitrary genus

✍ Scribed by Saburo Higuchi


Book ID
117556669
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
504 KB
Volume
540
Category
Article
ISSN
0550-3213

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πŸ“œ SIMILAR VOLUMES


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A digraph with n vertices and fixed outdegree m is generated randomly so that each such digraph is equally likely to be chosen. We consider the probability of the existence of a Hamiltonian cycle in the graph obtained by ignoring arc orientation. We show that there exists m (~23) such that a Hamilto

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Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set

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✍ JΓ‘nos KomlΓ³s; Endre SzemerΓ©di πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 874 KB

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