Allen, Peter
(2010)
*Dense H-free graphs are almost (χ(H)−1)-partite.*
The Electronic Journal of Combinatorics, 27
(R21).
ISSN 1077-8926

## Abstract

By using the Szemerédi Regularity Lemma, Alon and Sudakov recently extended the classical Andrásfai-Erdős-Sós theorem to cover general graphs. We prove, without using the Regularity Lemma, that the following stronger statement is true. Given any (r+1)-partite graph H whose smallest part has t vertices, there exists a constant C such that for any given ε>0 and sufficiently large n the following is true. Whenever G is an n-vertex graph with minimum degree δ(G)≥(1−33r−1+ε)n, either G contains H, or we can delete f(n,H)≤Cn2−1t edges from G to obtain an r-partite graph. Further, we are able to determine the correct order of magnitude of f(n,H) in terms of the Zarankiewicz extremal function.

Item Type: | Article |
---|---|

Official URL: | http://www.combinatorics.org/ojs/index.php/eljc/in... |

Additional Information: | © 2010 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: | 28 May 2012 14:43 |

URL: | http://eprints.lse.ac.uk/44096/ |

### Actions (login required)

Record administration - authorised staff only |