Abstract:Tverberg's theorem is a classic result in discrete geometry. It states that for any integer k ≥ 2 and any finite d-dimensional point set P ⊂ R d of at least (d + 1)(k − 1) + 1 points, we can partition P into k subsets whose convex hulls have a non-empty intersection. The computational problem of finding such a partition lies in the complexity class PPAD ∩ PLS, but no hardness results are known. Tverberg's theorem also has a colorful variant: the points in P have colors, and under certain conditions, P can be p… Show more
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