发表机构
Soochow University; University of Science and Technology of China（苏州大学; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明对任意非负整数r，长度至少1665r+1454且含r个方向翻转的定向路径均为竞赛图反Sidorenko，推广了已有结果。
AI 中文摘要
一个定向图$H$被称为竞赛图反Sidorenko（TAS），如果均匀随机竞赛图在所有竞赛图中渐近地最大化$H$的同态密度。对于定向路径$P$，方向翻转是指非叶子的源或汇。Sah、Sawhney和Zhao证明了方向一致的路径（没有方向翻转的路径）是TAS。He、Mani、Nie、Tung和Wei证明了对于$3\le k\le 7$，长度为$k$且恰好有一个方向翻转的每条定向路径都是TAS，并且Chen、Clemen和Noel最近将其推广到每个$k\ge 3$。在本文中，我们通过证明对于每个整数$r\ge 0$，长度为至少$1665r+1454$且具有$r$个方向翻转的每条定向路径都是竞赛图反Sidorenko的，从而推广了这些结果。
英文摘要
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 $3\le k\le 7$, every oriented path of length $k$ with exactly one direction flip is TAS, and Chen, Clemen and Noel recently extended this to every $k\ge 3$. In this paper, we extend these results by proving that for every integer $r\ge 0$, every oriented path of length at least $1665r+1454$ with $r$ direction flips is tournament anti-Sidorenko.
Comments22 pages
