### 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 language | English |
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Pages (from-to) | 1124-1135 |

Number of pages | 12 |

Journal | Journal of Applied Probability |

Volume | 47 |

Publication status | Published - 2010 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- power-law random graph
- clique
- greedy algorithm

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## Cite this

Janson, S., Luczak, T., & Norros, I. (2010). Large cliques in a power-law random graph.

*Journal of Applied Probability*,*47*, 1124-1135. http://www.vtt.fi/inf/julkaisut/muut/2010/0905.0561v1.pdf