%0 Journal Article %1 oliveros2025tverberg %A Oliveros, Deborah %A Roldán, Érika %A Soberón, Pablo %A Torres, Antonio J %D 2025 %J SIAM Journal on Discrete Mathematics %K Partition Tverberg nopdf graphs %N 2 %P 863--880 %R 10.1137/23M1610938 %T Tverberg Partition Graphs %V 39 %X 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 degrees of this graph, the number of vertices of maximal degree, its clique number, and its connectedness.

@article{oliveros2025tverberg, 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 degrees of this graph, the number of vertices of maximal degree, its clique number, and its connectedness.}, added-at = {2025-01-08T12:22:30.000+0100}, author = {Oliveros, Deborah and Roldán, Érika and Soberón, Pablo and Torres, Antonio J}, biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2777d0451ddc2fd763f9dff40f4c7f8f4/scadsfct}, doi = {10.1137/23M1610938}, eprint = {2310.08563}, interhash = {801625e74d266a26a740cf74abd22945}, intrahash = {777d0451ddc2fd763f9dff40f4c7f8f4}, journal = {SIAM Journal on Discrete Mathematics}, keywords = {Partition Tverberg nopdf graphs}, number = 2, pages = {863--880}, primaryclass = {math.CO}, timestamp = {2025-07-29T10:49:53.000+0200}, title = {Tverberg Partition Graphs}, volume = 39, year = 2025 }