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Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko
Abstract
An oriented graph H is said to be tournament anti-Sidorenko (TAS) if a uniformly random tournament asymptotically maximizes the homomorphism density of H among all tournaments. For an oriented path P, a direction flip is a non-leaf source or sink. Sah, Sawhney and Zhao proved that consistently directed paths (paths with no direction flips) are TAS. He, Mani, Nie, Tung and Wei proved that for 3≤ k≤ 7, every oriented path of length k with exactly one direction flip is TAS, and Chen, Clemen and Noel recently extended this to every k≥ 3. In this paper, we extend these results by proving that for every integer r≥ 0, every oriented path of length at least 1665r+1454 with r direction flips is tournament anti-Sidorenko.
Related
- On Tournament Anti-Sidorenko Orientations of Trees
- Every tournament T of order at least 3 admits infinitely many T-irregular oriented graphs
- Oriented paths with two blocks in bipartite oriented graphs
- Acyclic Dicolourings of Oriented Graphs: Paths, Random Tournaments, and Critical Orders
- Two-block paths in oriented graphs under the Ore-type condition
BibTeX
@misc{chen2026oriented,
title = {{Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko}},
author = {Hao Chen and Yupeng Lin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14655},
eprint = {2609.14655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14655},
}
RIS
TY - UNPB
TI - Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko
AU - Hao Chen
AU - Yupeng Lin
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14655
UR - https://arxiv.org/abs/2609.14655
AB - An oriented graph H is said to be tournament anti-Sidorenko (TAS) if a uniformly random tournament asymptotically maximizes the homomorphism density of H among all tournaments. For an oriented path P, a direction flip is a non-leaf source or sink. Sah, Sawhney and Zhao proved that consistently directed paths (paths with no direction flips) are TAS. He, Mani, Nie, Tung and Wei proved that for 3≤ k≤ 7, every oriented path of length k with exactly one direction flip is TAS, and Chen, Clemen and Noel recently extended this to every k≥ 3. In this paper, we extend these results by proving that for every integer r≥ 0, every oriented path of length at least 1665r+1454 with r direction flips is tournament anti-Sidorenko.
ER -