发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明有界双宽锦标赛是dχ-有界的，通过提出混合参数传递定理，结合有序图相关定理与障碍，解决了特定学者的猜想。
AI 中文摘要
对于锦标赛T和顶点序≺，令T≺为≺中后向弧构成的图。锦标赛的双团数为dω(T)=min≺ω(T≺)，双色数为dχ(T)=min≺χ(T≺)。我们证明了一个混合参数传递定理：对所有k和r，若tww(T)≤k且ω(T≺)≤r，则有序对(T≺,≺)的有序双宽由k和r的函数界定。证明结合了有序图的正则半网格定理与锦标赛中有界双宽的置换编码障碍。结合有界双宽图的多项式χ-有界性，这意味着有界双宽锦标赛被dω χ-有界，解决了Aboulker、Aubian、Charbit和Lopes的一个猜想。
英文摘要
For a tournament $T$ and a vertex ordering $\prec$, let $T^{\prec}$ be the graph of backward arcs in $\prec$. The diclique number of a tournament is $\domega(T)=\min_{\prec}ω(T^{\prec})$, and the dichromatic number is $\dchi(T)=\min_{\prec}χ(T^{\prec})$. We prove a mixed parameter transfer theorem: for all $k$ and $r$, if $\tww(T)\le k$ and $ω(T^{\prec})\le r$, then the ordered twin-width of $(T^{\prec},\prec)$ is bounded by a function of $k$ and $r$. The proof combines the regular-semigrid theorem for ordered graphs with permutation-encoding obstructions to bounded twin-width in tournaments. Together with polynomial $χ$-boundedness of graphs of bounded twin-width, this implies that tournaments of bounded twin-width are $\dchi$-bounded by $\domega$, resolving a conjecture of Aboulker, Aubian, Charbit, and Lopes.
