Brightwell, Graham, Panagiotou, Konstantinos and Steger, Angelika
(2007)
*On extremal subgraphs of random graphs.*
In: 18th ACM-SIAM Symposium on Discrete Algorithms, 7 - 9 January, New Orleans, Louisiana.

## Abstract

Let K-l denote the complete graph on vertices. We prove that there is a constant c = c(l) > 0, such that whenever p >= n(-c), with probability tending to 1 when n goes to infinity, every maximum K-l-free subgraph of the binomial random graph G(n,p) is (l-1)-partite. This answers a question of Babai, Simonovits and Spencer [3]. The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with M edges, where M >> n, is nearly unique. More precisely, given a maximum cut C of G(n,m), we can obtain all maximum cuts by moving at most O (root n(3/)M) vertices between the parts of C.

Item Type: | Conference or Workshop Item (Paper) |
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Official URL: | http://www.siam.org/meetings/da07/ |

Additional Information: | © 2007 The Author |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 21 Oct 2010 13:40 |

URL: | http://eprints.lse.ac.uk/29718/ |

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