Title: Not colouring the 3-sphere
|Affiliation:||Unioversity of Waterloo|
Let S(3) be the graph formed by the unit vectors in R3, two vectors adjacent if they are orthogonal. I will prove that S(3) has no 3-colouring. The surprise is that the proof involves a detour through the theory of valuations of ﬁelds.
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