Large cliques in a power-law random graph

Svante Janson, Tomasz Luczak, Ilkka Norros

    Research output: Contribution to journalArticleScientificpeer-review

    22 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)1124-1135
    Number of pages12
    JournalJournal of Applied Probability
    Volume47
    Publication statusPublished - 2010
    MoE publication typeA1 Journal article-refereed

    Keywords

    • power-law random graph
    • clique
    • greedy algorithm

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