ar X iv : 0 90 5 . 05 61 v 1 [ m at h . C O ] 5 M ay 2 00 9 LARGE CLIQUES IN A POWER - LAW RANDOM GRAPH

Abstract

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 whp 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 whp finds in G(n, α) a large clique of size (1 + o(1))ω(G(n, α)) in polynomial time.

Cite this paper

@inproceedings{Janson2009arXI, title={ar X iv : 0 90 5 . 05 61 v 1 [ m at h . C O ] 5 M ay 2 00 9 LARGE CLIQUES IN A POWER - LAW RANDOM GRAPH}, author={Svante Janson and Tomasz Luczak and Ilkka Norros}, year={2009} }