Skip to main content
Log in

A universal bound concerning t-intersecting families

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

A very short inductive proof is given for the maximal size of a k-graph on n vertices in which any two edges overlap in at least t vertices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Ahlswede and L. H. Khachatrian, The complete intersection theorem for systems of finite sets, Eur. J. Comb., 18, 2 (1997), 125–136.

  2. P. Erdős, C. Ko and R. Rado, Intersection theorems for systems of finite sets, Quart. J. Math. Oxford Ser. (2), 12 (1961), 313–320.

  3. P. Frankl, The Erdős–Ko–Rado theorem is true for n = ckt, in: Combinatorics, Proc.Fifth Hungarian Colloq. (Keszthely, 1976), vol. I, Colloq. Math. Soc. János Bolyai, vol. 18, North-Holland, (Amsterdam–New York, 1978), pp. 365–375.

  4. P. Frankl, The shifting techniques in extremal set theory, in: Surveys in Combinatorics, LMS Lecture Note Series, vol. 123, Cambridge Univ. Press (1987), pp. 81–110.

  5. P. Frankl, An improved universal bound for t-intersecting families, European J. Combin., 87(2020), 103134, 4 pp.

  6. R. M. Wilson, The exact bound in the Erdős–Ko–Rado theorem, Combinatorica, 4(1984), 247–257.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Frankl.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Frankl, P. A universal bound concerning t-intersecting families. Acta Math. Hungar. 171, 200–202 (2023). https://doi.org/10.1007/s10474-023-01373-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-023-01373-z

Key words and phrases

Mathematics Subject Classification

Navigation