Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-30T20:27:58.637Z Has data issue: false hasContentIssue false
  • English
  • Français

The Turán Number of F3,3

Published online by Cambridge University Press:  29 November 2011

PETER KEEVASH  and
DHRUV MUBAYI
PETER KEEVASH
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (e-mail: [email protected])
DHRUV MUBAYI
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, IL 60607, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Let F3,3 be the 3-graph on 6 vertices, labelled abcxyz, and 10 edges, one of which is abc, and the other 9 of which are all triples that contain 1 vertex from abc and 2 vertices from xyz. We show that for all n ≥ 6, the maximum number of edges in an F3,3-free 3-graph on n vertices is . This sharpens results of Zhou [9] and of the second author and Rödl [7].

Keywords

Primary 05C3505C65
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 3 , May 2012 , pp. 451 - 456
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bondy, A. and Tuza, Z. (1997) A weighted generalization of Turán's theorem. J. Graph Theory 25 267–275.3.0.CO;2-I>CrossRefGoogle Scholar
[2]de Caen, D. and Füredi, Z. (2000) The maximum size of 3-uniform hypergraphs not containing a Fano plane. J. Combin. Theory Ser. B 78 274–276.CrossRefGoogle Scholar
[3]Füredi, Z. and Kündgen, A. (2002) Turán problems for integer-weighted graphs. J. Graph Theory 40 195–225.CrossRefGoogle Scholar
[4]Goldwasser, J. On the Turán number of {123,124,345}. Manuscript.Google Scholar
[5]Keevash, P. (2011) Hypergraph Turán problems. Surveys in Combinatorics 2011, to appear.CrossRefGoogle Scholar
[6]Keevash, P. and Mubayi, D. (2004) Stability theorems for cancellative hypergraphs. J. Combin. Theory Ser. B 92 163–175.CrossRefGoogle Scholar
[7]Mubayi, D. and Rödl, V. (2002) On the Turán number of triple systems. J. Combin. Theory Ser. A 100 136–152.CrossRefGoogle Scholar
[8]Turán, P. (1961) Research problem. Közl MTA Mat. Kutató Int. 6 417–423.Google Scholar
[9]Zhou, B. (1991) A Turán-type problem on 3-graphs. Ars Combin. 31 177–181.Google Scholar