Source: J. Appl. Probab.
Volume 47, Number 4
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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