Brightwell, Graham, Panagiotou, Konstantinos and Steger, Angelika
(2012)
*Extremal subgraphs of random graphs.*
Random Structures and Algorithms, 41
(2).
pp. 147-178.
ISSN 1042-9832

## Abstract

We prove that there is a constant c > 0, such that whenever p ≥ n -c, with probability tending to 1 when n goes to infinity, every maximum triangle-free subgraph of the random graph G n,p is bipartite. This answers a question of Babai, Simonovits and Spencer (Babai et al., J Graph Theory 14 (1990) 599-622). 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 and M ≤ (n 2)/2, 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(√n 3/M) vertices between the parts of C.

Item Type: | Article |
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Official URL: | http://onlinelibrary.wiley.com/journal/10.1002/(IS... |

Additional Information: | © 2012 Wiley |

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

Sets: | Departments > Mathematics |

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

Date Deposited: | 16 Apr 2012 11:26 |

URL: | http://eprints.lse.ac.uk/43043/ |

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