### Abstract

We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph G(n, 1/2), and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kučera. In this paper we present an efficient algorithm for all k > cn^{0.5}, for any fixed c > 0, thus improving the trivial case k > cn^{0.5}(log n)^{0.5}. The algorithm is based on the spectral properties of the graph.

Original language | English (US) |
---|---|

Pages (from-to) | 457-466 |

Number of pages | 10 |

Journal | Random Structures and Algorithms |

Volume | 13 |

Issue number | 3-4 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Finding a large hidden clique in a random graph'. Together they form a unique fingerprint.

## Cite this

*Random Structures and Algorithms*,

*13*(3-4), 457-466. https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w