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Tverberg's theorem says that a set with sufficiently many points in$\mathbb{R}^d$ can always be partitioned into $m$ parts so that the$(m-1)$-simplex is the (nerve) intersection pattern of the convex hulls of theparts. The main results of our paper demonstrate that Tverberg's theorem is buta special case of a more general situation. Given sufficiently many points, alltrees and cycles can also be induced by at least one partition of a point set.

Tverberg-Type Theorems with Trees and Cycles as (Nerve) Intersection Patterns