Result: Tverberg Partition Graphs: Tverberg partition graphs
Title:
Tverberg Partition Graphs: Tverberg partition graphs
Authors:
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
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1095-7146
0895-4801
0895-4801
DOI:
10.1137/23m1610938
DOI:
10.48550/arxiv.2310.08563
Access URL:
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....ef2c761570a99eab5a55b85cd6a7a02b
Database:
OpenAIRE
Further Information
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.