English

Decomposition of tournament limits

Combinatorics 2017-12-11 v1 Probability

Abstract

The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We prove that each tournament kernel and each tournament limit can be decomposed into a direct sum of irreducible components, with transitive components interlaced. We also show that this decomposition is essentially unique.

Keywords

Cite

@article{arxiv.1604.04271,
  title  = {Decomposition of tournament limits},
  author = {Erik Thörnblad},
  journal= {arXiv preprint arXiv:1604.04271},
  year   = {2017}
}

Comments

31 pages; 3 figures

R2 v1 2026-06-22T13:32:47.745Z