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arXiv · 2602.14008

On the supersaturation of oriented Tur\'an problems

Xuanrui Hu·Yuefang Sun
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Abstract

The oriented Tur\'{a}n number of a given oriented graph $\overrightarrow{F}$, denoted by $\exo(n,\overrightarrow{F})$, is the largest number of arcs in $n$-vertex $\overrightarrow{F}$-free oriented graphs. This parameter could be seen as a natural oriented version of the classical Tur\'{a}n number. In this paper, we study the supersaturation phenomenon for oriented Tur\'{a}n problems, and prove oriented versions of the famous Erd\H{o}s-Simonovits Supersaturation Theorem and Moon-Moser inequality, and supersaturation theorems for tournaments and antidirected complete bipartite graphs.

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Xuanrui Hu, Yuefang Sun. 2026-02-15. On the supersaturation of oriented Tur\'an problems. https://arxiv.org/abs/2602.14008

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