Skip to main content
SpringerLink
Log in

The Maximum Size of 3-Wise Intersecting and 3-Wise Union Families

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Let be an n-uniform hypergraph on 2n vertices. Suppose that and holds for all F1,F2,F3 ∈ . We prove that the size of is at most .

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Engel, K., Gronau, H.-D.O.F.: An Erdős–Ko–Rado type theorem II. Acta Cybernet. 4, 405–411 (1986)

    Google Scholar 

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

    Google Scholar 

  3. Frankl, P.: On Sperner families satisfying an additional condition. J. Combin. Theory (A) 20, 1–11 (1976)

    Google Scholar 

  4. Frankl, P., Tokushige, N.: Weighted 3-wise 2-intersecting families. J. Combin. Theory (A) 100, 94–115 (2002)

    Google Scholar 

  5. Frankl, P., Tokushige, N.: Random walks and multiply intersecting families. J. Combin. Theory (A) 109, 121–134 (2005)

    Google Scholar 

  6. Gronau, H.-D.O.F.: An Erdős–Ko–Rado type theorem. Finite and infinite sets, Vol. I, II (Eger, 1981). Colloq Math Soc J Bolyai 37, 333–342 (1984)

    Google Scholar 

  7. Tokushige, N.: A frog's random jump and the Pólya identity. Ryukyu Math Journal 17, 89–103 (2004)

    Google Scholar 

  8. Tokushige, N.: The maximum size of 4-wise 2-intersecting and 4-wise 2-union families. European J. Combin (in press)

Download references

Author information

Authors and Affiliations

  1. CNRS, ER 175 Combinatoire, 2 Place Jussieu, 75005, Paris, France

    Peter Frankl

  2. College of Education, Ryukyu University, Nishihara, Okinawa, 903-0213, Japan

    Norihide Tokushige

Authors
  1. Peter Frankl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Norihide Tokushige
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Frankl.

Additional information

The second author was supported by MEXT Grant-in-Aid for Scientific Research (B) 16340027

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frankl, P., Tokushige, N. The Maximum Size of 3-Wise Intersecting and 3-Wise Union Families. Graphs and Combinatorics 22, 225–231 (2006). https://doi.org/10.1007/s00373-006-0655-2

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-006-0655-2

Keywords

Search

Navigation