A note on Hedetniemi's conjecture, Stahl's conjecture and the Poljak-Rödl function

Claude Tardif, Xuding Zhu

We prove that $\min \{\chi (G),\chi (H)\}-\chi (G\times H)$ can be arbitrarily large, and that if Stahl's conjecture on the multichromatic number of Kneser graphs holds, then $\min\{χ(G), χ(…