Skip to main content
SpringerLink
Log in

The chromatic number of the product of two ℵ1-chromatic graphs can be countable

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

We prove (in ZFC) that for every infinite cardinal ϰ there are two graphsG 0,G 1 with χ(G 0)=χ(G 1)=ϰ+ and χ(G 0×G 1)=ϰ. We also prove a result from the other direction. If χ(G 0)≧≧ℵ0 and χ(G 1)=k<ω, then χ(G 0×G 1)=k.

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. M. El-Zahar, N. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4.Combinatorica,5 (1985).

  2. S. T. Hedetniemi, Homomorphisms of graphs and automata,Univ. of Michigan Technical Report 03 105-44-T, 1966.

  3. S. Todorčević, Stationary sets, Trees and Continuums,Publ. Inst. Math. (Beograd) 27 (41) (1981), 249–262.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary

    A. Hajnal

Authors
  1. A. Hajnal
    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

Hajnal, A. The chromatic number of the product of two ℵ1-chromatic graphs can be countable. Combinatorica 5, 137–139 (1985). https://doi.org/10.1007/BF02579376

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579376

AMS subject classification (1980)

Search

Navigation