Abstract
Given a finite set of points in $\mathbb\R\^d$, Tverberg's
theorem guarantees the existence of partitions of this set
into parts whose convex hulls intersect. We introduce a graph
structured on the family of Tverberg partitions of a given
set of points, whose edges describe closeness between
different Tverberg partitions. We prove bounds on the minimum
and maximum degree of this graph, the number of vertices of
maximal degree, its clique number, and its connectedness.
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