## Claude Tardif

*The chromatic number of the product of two graphs is at least half the minimum of the fractional chromatic numbers of the factors *

Comment.Math.Univ.Carolinae 42,2 (2001) 353-355. **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

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