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Distribution of the number of nonappearing lengths of cycles in a random mapping

✍ Scribed by A. S. Ambrosimov

Publisher
SP MAIK Nauka/Interperiodica
Year
1978
Tongue
English
Weight
166 KB
Volume
23
Category
Article
ISSN
0001-4346

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Let a random graph G be constructed by adding random edges one by one, starting with n isolated vertices. We show that with probability going to one as n goes to infinity, when G first has minimum degree two, it has at least (log n)('-')" distinct hamilton cycles for any fixed E > 0.

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Bondy and Vince proved that every graph with minimum degree at least three contains two cycles whose lengths differ by one or two, which answers a question raised by Erdo ˝s. By a different approach, we show in this paper that if G is a graph with minimum degree d(G) \ 3k for any positive integer k,