Year: 2026
Type: preprint
Abstract: Very recently, using Meshulam's lemma, Blagojević proved a constrained version of the colorful Carathéodory theorem for joins of bipartite spanning trees and wedge of spheres. Our main contribution extends his result from joins of bipartite spanning trees with wedges of spheres to joins of spanning \(k\)-trees with wedges of spheres. Our proof is elementary and avoids the topological machinery. We also discuss a homological variation of spanning \(k\)-trees and some Carathéodory-type results for them.
Source: arXiv (Cornell University)
Authors: Bludov, Mikhail, Polyanskii, Alexander
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167059920