Combinatorica

, Volume 5, Issue 2, pp 137–139 | Cite as

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

  • A. Hajnal
Article

Abstract

We prove (in ZFC) that for every infinite cardinal ϰ there are two graphsG0,G1 with χ(G0)=χ(G1)=ϰ+ and χ(G0×G1)=ϰ. We also prove a result from the other direction. If χ(G0)≧≧ℵ0 and χ(G1)=k<ω, then χ(G0×G1)=k.

AMS subject classification (1980)

05 C 15 04 A 05 04 A 10 04 A 20 

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References

  1. [1]
    M. El-Zahar, N. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4.Combinatorica,5 (1985).Google Scholar
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    S. T. Hedetniemi, Homomorphisms of graphs and automata,Univ. of Michigan Technical Report 03 105-44-T, 1966.Google Scholar
  3. [3]
    S. Todorčević, Stationary sets, Trees and Continuums,Publ. Inst. Math. (Beograd) 27 (41) (1981), 249–262.Google Scholar

Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

  • A. Hajnal
    • 1
  1. 1.The Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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