Academic Journal
Tverberg Partition Graphs: Tverberg partition graphs
| Title: | Tverberg Partition Graphs: Tverberg partition graphs |
|---|---|
| Authors: | Deborah Oliveros, Érika Roldán, Pablo Soberón, Antonio J. Torres |
| Source: | SIAM Journal on Discrete Mathematics. 39:863-880 |
| Publication Status: | Preprint |
| Publisher Information: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Extremal problems in graph theory, Other problems of combinatorial convexity, flip graphs, Enumeration in graph theory, Helly-type theorems and geometric transversal theory, partition graph, discrete configuration spaces, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, reconfiguration problems, Mathematics - Combinatorics, Tverberg's theorem, Combinatorics (math.CO), combinatorial geometry |
| Description: | 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. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/23m1610938 |
| DOI: | 10.48550/arxiv.2310.08563 |
| Access URL: | http://arxiv.org/abs/2310.08563 https://zbmath.org/8037177 https://doi.org/10.1137/23m1610938 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....ef2c761570a99eab5a55b85cd6a7a02b |
| Database: | OpenAIRE |
| ISSN: | 10957146 08954801 |
|---|---|
| DOI: | 10.1137/23m1610938 |