Academic Journal
Tverberg Partition Graphs: Tverberg partition graphs
| Τίτλος: | Tverberg Partition Graphs: Tverberg partition graphs |
|---|---|
| Συγγραφείς: | Deborah Oliveros, Érika Roldán, Pablo Soberón, Antonio J. Torres |
| Πηγή: | SIAM Journal on Discrete Mathematics. 39:863-880 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Society for Industrial & Applied Mathematics (SIAM), 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | 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 |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/23m1610938 |
| DOI: | 10.48550/arxiv.2310.08563 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2310.08563 https://zbmath.org/8037177 https://doi.org/10.1137/23m1610938 |
| Rights: | arXiv Non-Exclusive Distribution |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....ef2c761570a99eab5a55b85cd6a7a02b |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 10957146 08954801 |
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| DOI: | 10.1137/23m1610938 |