, Volume 5, Issue 2, pp 137–139

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

  • A. Hajnal

DOI: 10.1007/BF02579376

Cite this article as:
Hajnal, A. Combinatorica (1985) 5: 137. doi:10.1007/BF02579376


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 1504 A 0504 A 1004 A 20

Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

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