Skip to main content
SpringerLink
Log in

Size-Maximal Symmetric Difference-Free Families of Subsets of [n]

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Union-free families of subsets of [n] = {1, . . . , n} have been studied in Frankl and Füredi (Eur J Combin 5:127–131, 1984). In this paper, we provide a complete characterization of maximal symmetric difference-free families of subsets of [n].

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. http://en.wikipedia.org/wiki/Union-closed_sets_conjecture

  2. Babai L., Sos V.T.: Sidon sets in groups and induced subgraphs of Cayley graphs. Eur. J. Combin. 1, 1–11 (1985)

    MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  4. Frankl P., Füredi Z.: Union-free hypergraphs and probability theory. Eur. J. Combin. 5, 127–131 (1984)

    Article  MATH  Google Scholar 

  5. O’Bryant, K.: A complete annotated bibliography of work related to Sidon sequences. Electr. J. Combin. Dynamical Survey #DS11. http://www.combinatorics.org/Surveys/ds11.pdf (2004)

  6. Sperner E.: Ein Satz über Untermengen einer endlichen Menge. Math. Zeitschrift 27, 544–548 (1928)

    Article  MATH  MathSciNet  Google Scholar 

  7. West D.: Introduction to Graph Theory, 2nd edn. Prentice Hall, New Jersey (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, East Tennessee State University, Johnson City, USA

    Travis G. Buck & Anant P. Godbole

Authors
  1. Travis G. Buck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anant P. Godbole
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anant P. Godbole.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buck, T.G., Godbole, A.P. Size-Maximal Symmetric Difference-Free Families of Subsets of [n]. Graphs and Combinatorics 30, 101–108 (2014). https://doi.org/10.1007/s00373-012-1255-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-012-1255-y

Keywords

Search

Navigation