L. Soukup

Hedetniemi's Conjecture for Uncountable Complementary Graphs

We study the complementary version of Hedetniemi's problem for infinite graphs. We prove that if a graph $G$ and its complement $\overline{G}$ are both uncountably chromatic while their categorical product is countably chromatic, then $|V(G)|=\omega_1$. Assuming $\diamondsuit$, we construct a graph $G$ on $\omega_1$ su...