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.
|Number of pages||12|
|Journal||Journal of Applied Probability|
|Publication status||Published - 2010|
|MoE publication type||A1 Journal article-refereed|
- power-law random graph
- greedy algorithm