Allen, Peter 
ORCID: 0000-0001-6555-3501
(2010)
Dense H-free graphs are almost (χ(H)−1)-partite.
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 |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 28 May 2012 14:43 |
| Last Modified: | 11 Dec 2024 23:48 |
| URI: | http://eprints.lse.ac.uk/id/eprint/44096 |
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