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arXiv · 2507.13267

On the Turánability and tileability of oriented graphs

Igor Araujo·Zimu Xiang
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Abstract

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

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Igor Araujo, Zimu Xiang. 2026-03-18. On the Turánability and tileability of oriented graphs. https://arxiv.org/abs/2507.13267

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