Abstract:One consequence of Hedetniemi's conjecture on the chromatic number of the product of graphs is that the bound $\chi (G \times H) \geq \min \{ \chi _f(G), \chi _f(H) \}$ should always hold. We prove that $\chi (G \times H) \geq \frac {1}{2} \min \{ \chi _f(G), \chi _f(H) \}$.
Keywords: Hedetniemi's conjecture, (fractional) chromatic number
AMS Subject Classification: 05C15