A hypergraph regularity method for generalised Turan problems
| dc.creator | Keevash, Peter | |
| dc.date | 2008-09-22 | |
| dc.date.accessioned | 2026-07-07T10:04:24Z | |
| dc.date.available | 2026-07-07T10:04:24Z | |
| dc.description | We describe a method that we believe may be foundational for a comprehensive theory of generalised Turan problems. The cornerstone of our approach is a quasirandom counting lemma for quasirandom hypergraphs, which extends the standard counting lemma by not only counting copies of a particular configuration but also showing that these copies are evenly distributed. We demonstrate the power of the method by proving a conjecture of Mubayi on the codegree threshold of the Fano plane, that any 3-graph on n vertices for which every pair of vertices is contained in more than n/2 edges must contain a Fano plane, for n sufficiently large. For projective planes over fields of odd size q we show that the codegree threshold is between n/2-q+1 and n/2, but for PG_2(4) we find the somewhat surprising phenomenon that the threshold is less than (1/2-c)n for some small c>0. We conclude by setting out a program for future developments of this method to tackle other problems. | |
| dc.description | 43 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0809.3674 | |
| dc.identifier | http://arxiv.org/abs/0809.3674 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169661 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C35, 05C65 | |
| dc.title | A hypergraph regularity method for generalised Turan problems | |
| dc.type | text |