### Abstract

Original language | English |
---|---|

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 |

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### Keywords

- power-law random graph
- clique
- greedy algorithm

### Cite this

*Journal of Applied Probability*,

*47*, 1124-1135.

}

*Journal of Applied Probability*, vol. 47, pp. 1124-1135.

**Large cliques in a power-law random graph.** / Janson, Svante; Luczak, Tomasz; Norros, Ilkka.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Large cliques in a power-law random graph

AU - Janson, Svante

AU - Luczak, Tomasz

AU - Norros, Ilkka

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - power-law random graph

KW - clique

KW - greedy algorithm

UR - https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F1CE6D1654D53B7CE7C4665D5BD04D4A/S0021900200007415a.pdf/large_cliques_in_a_powerlaw_random_graph.pdf

M3 - Article

VL - 47

SP - 1124

EP - 1135

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

ER -