# Tverberg’s Theorem, Disks, and Hamiltonian Cycles

@article{Soberon2021TverbergsTD,
title={Tverberg’s Theorem, Disks, and Hamiltonian Cycles},
author={Pablo Sober'on and Yaqian Tang},
journal={Annals of Combinatorics},
year={2021}
}
• Published 24 November 2020
• Mathematics
• Annals of Combinatorics
For a finite set of $S$ points in the plane and a graph with vertices on $S$ consider the disks with diameters induced by the edges. We show that for any odd set $S$ there exists a Hamiltonian cycle for which these disks share a point, and for an even set $S$ there exists a Hamiltonian path with the same property. We discuss high-dimensional versions of these theorems and their relation to other results in discrete geometry.
4 Citations

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