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Tverberg Partition Graphs

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arxiv 2310.08563 v1 pith:7BZNX5BN submitted 2023-10-12 math.CO

Deborah Oliveros , Érika Roldán , Pablo Soberón , Antonio J. Torres This is my paper · ORCID
classification math.CO
keywords tverbergpartitionsdegreegivengraphnumberpointswhose
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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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