On Tournament Anti-Sidorenko Orientations of Trees

@misc{chen2026tournament,
  title = {{On Tournament Anti-Sidorenko Orientations of Trees}},
  author = {Hao Chen and Felix Christian Clemen and Jonathan A. Noel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.14138},
  eprint = {2605.14138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.14138},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - On Tournament Anti-Sidorenko Orientations of Trees
AU  - Hao Chen
AU  - Felix Christian Clemen
AU  - Jonathan A. Noel
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2605.14138
UR  - https://arxiv.org/abs/2605.14138
AB  - An oriented graph H⃗ is said to be tournament anti-Sidorenko if the homomorphism density of H⃗ in any tournament T⃗ is bounded above by the homomorphism density of H⃗ in a large uniformly random tournament. We prove the following: (1) Every oriented path with at least three arcs and exactly one non-leaf source or sink vertex is tournament anti-Sidorenko. (2) An oriented path is tournament anti-Sidorenko if the distance between any leaf vertex and any source or sink vertex is at least two and the distance between any pair of non-leaf source or sink vertices is a multiple of four. (3) Every spider with exactly three legs admits a tournament anti-Sidorenko orientation. The first result proves a conjecture posed by He, Mani, Nie, Tung and Wei. The third resolves a problem from the same paper, in fact establishing a substantially more general statement, and provides evidence in support of a conjecture of Fox, Himwich, Mani and Zhou. The second yields the first family of tournament anti-Sidorenko oriented paths which is exponentially large with respect to the number of arcs.
ER  -