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It is proved that in Gödel's constructible universe, for every infinite successor cardinal , there exist graphs and of size and chromatic number , for which the product graph is countably chromatic.
In particular, this provides an affirmative answer to a question of Hajnal from 1985.
Cite this article
Assaf Rinot, Hedetniemi's conjecture for uncountable graphs. J. Eur. Math. Soc. 19 (2017), no. 1, pp. 285–298DOI 10.4171/JEMS/666