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Cycles in random graphs

✍ Scribed by Tomasz Łuczak

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
348 KB
Volume
98
Category
Article
ISSN
0012-365X

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✦ Synopsis

tuczak, T., Cycles in random graphs, Discrete Mathematics 98 (1991) 231-236. Let G(n, p) be a graph on n vertices in which each possible edge is presented independently with probability p = p(n) and u'(n, p) denote the number of vertices of degree 1 in G(n, p). It is shown that if E > 0 and rip(n)))) a~ then the probability that G(n, p) contains cycles of all lengths r, 3 G r < n -(1 + c)u'(n, p), tends to 1 as n+ m.

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