Tensor products of graphs can require fewer colors than their factors: https://arxiv.org/abs/1905.02167
This short new preprint by Yaroslav Shitov gives counterexamples to Hedetniemi’s conjecture (https://en.wikipedia.org/wiki/Hedetniemi%27s_conjecture) from 1966. In a new blog post (https://gilkalai.wordpress.com/2019/05/10/sansation-in-the-morning-news-yaroslav-shitov-counterexamples-to-hedetniemis-conjecture/) Gil Kalai explains the construction.
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