Hedetniemi's conjecture for uncountable graphs

  • Assaf Rinot

    Bar-Ilan University, Ramat Gan, Israel


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. 285–298

DOI 10.4171/JEMS/666