English

On the Tur\'anability and tileability of oriented graphs

Combinatorics 2026-03-20 v2

Abstract

An oriented graph HH is Tur\'anable (resp. tileable) if there exist n0Nn_0 \in \mathbb{N} such that every semi-regular near-tournament on nn0n \ge n_0 vertices contains a copy of HH (resp. a perfect HH-tiling). We disprove a conjectured characterization of Tur\'anable oriented graphs by DeBiasio, Han, Lo, Molla, Piga, and Treglown, show that there are Tur\'anable oriented graphs which are not tileable, and provide a new example of tileable oriented graph.

Keywords

Cite

@article{arxiv.2507.13267,
  title  = {On the Tur\'anability and tileability of oriented graphs},
  author = {Igor Araujo and Zimu Xiang},
  journal= {arXiv preprint arXiv:2507.13267},
  year   = {2026}
}
R2 v1 2026-07-01T04:06:26.063Z