Spanning k-trees and the colorful Carathéodory theorem

@misc{bludov2026spanning,
  title = {{Spanning \(k\)-trees and the colorful Carathéodory theorem}},
  author = {Mikhail Bludov and Alexander Polyanskii},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2607.01143},
  eprint = {2607.01143},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.01143},
}

TY  - UNPB
TI  - Spanning k-trees and the colorful Carathéodory theorem
AU  - Mikhail Bludov
AU  - Alexander Polyanskii
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2607.01143
UR  - https://arxiv.org/abs/2607.01143
AB  - 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.
ER  -