The Chromatic Number of the Product of 5-Chromatic Graphs can be 4

We show that for any integers m_1, m_2 ≥ 5 , there exist graphs G , H such that χ (G) = m_1 , χ (H) = m_2 and χ (G × H) < min{m_1, m_2} . In particular for m_1 = m_2 = 5 , this settles the last remaining open case of Hedetniemi’s conjecture.