Partitioning a tournament into sub-tournaments of high connectivity

António Girão; Shoham Letzter

Partitioning a tournament into sub-tournaments of high connectivity

Combinatorics 2025-06-04 v4

Authors: António Girão , Shoham Letzter

Abstract

We prove that there exists a constant $c > 0$ such that the vertices of every strongly $c \cdot kt$ -connected tournament can be partitioned into $t$ parts, each of which induces a strongly $k$ -connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of K\"uhn, Osthus and Townsend (2016).

Keywords

tournament strong connectivity vertex partition extremal graph theory conjecture

Cite

@article{arxiv.2210.17371,
  title  = {Partitioning a tournament into sub-tournaments of high connectivity},
  author = {António Girão and Shoham Letzter},
  journal= {arXiv preprint arXiv:2210.17371},
  year   = {2025}
}

Comments

25 pages, 2 figures, clarified proof of Proposition 3.1

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