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