On the Tur\'anability and tileability of oriented graphs
Combinatorics
2026-03-20 v2
Abstract
An oriented graph is Tur\'anable (resp. tileable) if there exist such that every semi-regular near-tournament on vertices contains a copy of (resp. a perfect -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}
}