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arXiv · 2310.08563

Tverberg Partition Graphs

Deborah Oliveros·Érika Roldán·Pablo Soberón·Antonio J. Torres
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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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Deborah Oliveros, Érika Roldán, Pablo Soberón, Antonio J. Torres. 2023-10-12. Tverberg Partition Graphs. https://arxiv.org/abs/2310.08563

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