Large cliques in a power-law random graph
Svante Janson, Tomasz Łuczak, and Ilkka Norros
Source: J. Appl. Probab. Volume 47, Number 4
(2010), 1124-1135.
Abstract
In this paper we study the size of the largest clique ω(G(n, α)) in a random graph G(n, α) on n vertices which has power-law degree distribution with exponent α. We show that, for `flat' degree sequences with α > 2, with high probability, the largest clique in G(n, α) is of a constant size, while, for the heavy tail distribution, when 0 < α < 2, ω(G(n, α)) grows as a power of n. Moreover, we show that a natural simple algorithm with high probability finds in G(n, α) a large clique of size (1 - o(1))ω(G(n, α)) in polynomial time.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1294170524
Digital Object Identifier: doi:10.1239/jap/1294170524
Zentralblatt MATH identifier: 05835873
Mathematical Reviews number (MathSciNet): MR2752885
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Journal of Applied Probability
