Hedetniemi’s conjecture for uncountable graphs

Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal{G}$ and $\mathcal{H}$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal{G}\times \mathcal{H}$ is countably chromatic.

with Sauer and Hajnal, Budapest, August 2005

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A. Rinot, Hedetniemi’s conjecture for uncountable graphs, J. Eur. Math. Soc., 19(1): 285-298, 2017.