The [Hedetniemi's conjecture](https://en.wikipedia.org/wiki/Hedetniemi%27s_conjecture) was proposed in 1966. It stated that the chromatic number of the tensor product of two graph $G$ and $H$ is equal to the minimum of the individual chromatic numbers of the graphs $G$ and $H$. This conjecture was disproved by giving an explicit counterexample, by Yaroslav Shitov in 2019 in this [paper](https://annals.math.princeton.edu/2019/190-2/p06 "Yaroslav Shitov: Counterexamples to Hedetniemi’s conjecture") published in Annals of Mathematics.