Thread 1/7 As I mentioned last night, it looks like Hedetniemi's conjecture (HC) has indeed been refuted, in a preprint posted earlier this week by Yaroslav Shitov on arXiv: arxiv.org/abs/1905.02167 Experts have now looked at this 3-page paper and agree that it appears correct.
2/7 HC has to do with graph coloring certain product graphs. In this short thread, I'll give some background on the conjecture. Good surveys exist on the conjecture written independently by Sauer, Tardif, and Zhu. Or check out my Math Intelligencer paper with Nowakowski.
3/7 HC was first stated in: "Homomorphisms of graphs and automata", a technical report in 1966 U at the Michigan, submitted by Stephen Hedetnieimi, who was a grad student at the time. The conjecture was independently stated in by Burr, Erdos, and Lovasz in 1976.