Relatively small counterexamples to Hedetniemi's conjecture

Understand

Hedetniemi conjectured in 1966 that $\chi(G \times H) = \min\{\chi(G), \chi(H)\}$ for all graphs $G$ and $H$.

• Here $G\times H$ is the graph with vertex set $ V(G)\times V(H)$ defined by putting $(x,y)$ and $(x',y')$ adjacent if and only if $xx'\in E(G)$ and $yy'\in E(H)$.
• This conjecture received a lot of attention in the past half century.
• Recently, Shitov refuted this conjecture.