Skip to main content
SpringerLink
Log in

New estimates in the problem of the number of edges in a hypergraph with forbidden intersections

  • Large Systems
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

We improve the Frankl-Wilson upper bound on the maximal number of edges in a hypergraph with forbidden cardinalities of edge intersections.

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. Frankl, P. and Wilson, R., Intersection Theorems with Geometric Consequences, Combinatorica, 1981, vol. 1, no. 4, pp. 357–368.

    Article  MATH  MathSciNet  Google Scholar 

  2. Raigorodskii, A.M., Lineino-algebraicheskii metod v kombinatorike (Linear-Algebraic Method in Combinatorics), Moscow: MCCME, 2007.

    Google Scholar 

  3. Babai, L. and Frankl, P., Linear Algebra Methods in Combinatorics with Applications to Geometry and Computer Science, Preliminary version 2, Part 1, Department of Computer Science, Univ. of Chicago, 1992.

    Google Scholar 

  4. Bassalygo, L., Cohen, G., and Zémor, G., Codes with Forbidden Distances, Discrete Math., 2000, vol. 213, no. 1–3, pp. 3–11.

    Article  MATH  MathSciNet  Google Scholar 

  5. Raigorodskii, A.M., The Borsuk Problem and the Chromatic Numbers of Some Metric Spaces, Uspekhi Mat. Nauk, 2001, vol. 56, no. 1, pp. 107–146 [Russian Math. Surveys (Engl. Transl.), 2001, vol. 56, no. 1, pp. 103–139].

    Article  MathSciNet  Google Scholar 

  6. Raigorodskii, A.M., On the Chromatic Numbers of Spheres in Euclidean Spaces, Dokl. Akad. Nauk, 2010, vol. 432, no. 2, pp. 174–177 [Dokl. Math. (Engl. Transl.), 2010, vol. 81, no. 3, pp. 379–382].

    Google Scholar 

  7. Raigorodskii, A.M., On the Chromatic Numbers of Spheres in Rn, Combinbatorica, 2012, vol. 32, no. 1, pp. 111–123.

    Article  MATH  MathSciNet  Google Scholar 

  8. Kahn, J. and Kalai, G., A Counterexample to Borsuk’s Conjecture, Bull. Amer.Math. Soc. (N.S.), 1993, vol. 29, no. 1, pp. 60–62.

    Article  MATH  MathSciNet  Google Scholar 

  9. Raigorodskii, A.M., Three Lectures on the Borsuk Partition Problem, Surveys in Contemporary Mathematics, Young, N. and Choi, Y., Eds., London Math. Soc. Lect. Note Ser., vol. 347. Cambridge: Cambridge Univ. Press, 2007, pp. 202–248.

    Chapter  Google Scholar 

  10. Raigorodskii, A.M., Around the Borsuk Conjecture, Sovrem. Mat. Fundam. Napravl., 2007, vol. 23, pp. 147–164 [J. Math. Sci. (N.Y.) (Engl. Transl.), 2007, vol. 154, no. 4, pp. 604–623].

    Google Scholar 

  11. Raigorodskii, A.M., Coloring Distance Graphs and Graphs of Diameters, Thirty Essays on Geometric Graph Theory, Pach, J., Ed., Berlin: Springer, 2013, pp. 429–460.

    Chapter  Google Scholar 

  12. Raigorodskii, A.M., Counterexamples to Borsuk’s Conjecture on Spheres of Small Radius, Dokl. Akad. Nauk, 2010, vol. 434, no. 2, pp. 161–163 [Dokl. Math. (Engl. Transl.), 2010, vol. 82, no. 2, pp. 719–721].

    MathSciNet  Google Scholar 

  13. Raigorodskii, A.M., On Dimensionality in the Borsuk Problem, Uspekhi Mat. Nauk, 1997, vol. 52, no. 6, pp. 181–182 [Russian Math. Surveys (Engl. Transl.), 1997, vol. 52, no. 6, pp. 1324–1325].

    Article  MathSciNet  Google Scholar 

  14. Raigorodskii, A.M., On a Bound in the Borsuk Problem, Uspekhi Mat. Nauk, 1999, vol. 54, no. 2, pp. 185–186 [Russian Math. Surveys (Engl. Transl.), 1999, vol. 54, no. 2, pp. 453–454].

    Article  MathSciNet  Google Scholar 

  15. Raigorodskii, A.M., On the Chromatic Number of a Space, Uspekhi Mat. Nauk, 2000, vol. 55, no. 2, pp. 147–148 [Russian Math. Surveys (Engl. Transl.), 2000, vol. 55, no. 2, pp. 351–352].

    Article  MATH  MathSciNet  Google Scholar 

  16. Larman, D.G. and Rogers, C.A., The Realization of Distances within Sets in Euclidean Space, Mathematika, 1972, vol. 19, no. 1, pp. 1–24.

    MATH  MathSciNet  Google Scholar 

  17. Ahlswede, R. and Khachatrian, L.H., The Complete Nontrivial-Intersection Theorem for Systems of Finite Sets, J. Combin. Theory, Ser. A, 1996, vol. 76, no. 1, pp. 121–138.

    Article  MATH  MathSciNet  Google Scholar 

  18. Ahlswede, R. and Khachatrian, L.H., The Complete Intersection Theorem for Systems of Finite Sets, European J. Combin., 1997, vol. 18, no. 2, pp. 125–136.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Innovation and Higher Technology, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    E. I. Ponomarenko & A. M. Raigorodskii

  2. Mathematical Statistics and Random Processes Chair, Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, Russia

    A. M. Raigorodskii

Authors
  1. E. I. Ponomarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Raigorodskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. I. Ponomarenko.

Additional information

Original Russian Text © E.I. Ponomarenko, A.M. Raigorodskii, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 4, pp. 98–104.

Supported in part by the Russian Foundation for Basic Research, project no. 12-01-00683, President of the Russian Federation Grant no. MD-6277.2013.1, and Council for State Support of Leading Scientific Schools, grant no. NSh-2519.2012.1.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ponomarenko, E.I., Raigorodskii, A.M. New estimates in the problem of the number of edges in a hypergraph with forbidden intersections. Probl Inf Transm 49, 384–390 (2013). https://doi.org/10.1134/S0032946013040091

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946013040091

Keywords

Search

Navigation