Tverberg’s Theorem, Disks, and Hamiltonian Cycles

  title={Tverberg’s Theorem, Disks, and Hamiltonian Cycles},
  author={Pablo Sober'on and Yaqian Tang},
  journal={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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  • B. Birch
  • Mathematics, Philosophy
    Mathematical Proceedings of the Cambridge Philosophical Society
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