Skip to main content
SpringerLink
Log in

Colouring finite incidence structures

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

One of our results: Let ℙ denote a finite projective plane of ordern. Colour its vertices byχ colours. If no colour appears more than twice on any of the lines, thenχ ≥ n + 1. Explicit constructions show that this bound is sharp when ℙ is desarguesian.

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. Bose, R.C.: Mathematical theory of the symmetrical factorial design. Sankhyā8, 107–166 (1947)

    Google Scholar 

  2. deBruijin, N.G., Erdös, P.: On a combinatorial problem. Indagationes Math.10, 421–423 (1948)

    Google Scholar 

  3. Bruck, R.H.: Quadric extensions of cyclic planes. Proc. Symp. Appl. Math.X, 15–44. (1960)

    Google Scholar 

  4. Boros, E., Szönyi, T.: On the sharpness of a theorem of B. Segre, Combinatorica (to appear)

  5. Csima, J.: Colouring finite planes of odd order. Discrete Math.49, 309 (1984)

    Google Scholar 

  6. Erdös, P., Sós, V.T.: unpublished.

  7. Füredi, Z., Rosenberg, I.G.: Multicolored lines in a finite geometry. Discrete Math., submitted.

  8. Kabell, J.A.: A note on colorings of finite planes. Discrete Math.44, 319–320 (1983)

    Google Scholar 

  9. Lidl, R., Niederreider, H.: Finite Fields. pp. 278–289. Reading: Addison-Wesley 1983

    Google Scholar 

  10. Meshulam, R.: On multicolored lines in a linear space. J. Comb. Theory (A)40, 150–155 (1985)

    Google Scholar 

  11. Singer, J.: A theorem in finite projective geometry and some applications to number theory. Trans. Amer. Math. Soc.43, 377–385 (1938)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Math. and Stat., McMaster University, L8S4K1, Hamilton, Ontario, Canada

    J. Csima

  2. AT&T Bell Laboratories, Murray Hill, 2C-256, 07974, NJ, USA

    Z. Füredi

Authors
  1. J. Csima
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. Füredi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Csima, J., Füredi, Z. Colouring finite incidence structures. Graphs and Combinatorics 2, 339–346 (1986). https://doi.org/10.1007/BF01788107

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01788107

Keywords

Search

Navigation