AI 中文总结
该研究针对有向图，证明满足最小半度阈值及独立数条件的足够大的有向图包含指定长度的反有向环因子，其最小半度阈值渐近紧，采用了Ramsey-Turán型格吸收引理完成证明。
AI 中文摘要
设$C_{2s}^{\mathrm{ad}}$为长度为$2s$的反有向环，其中$s\geq2$。我们证明，对任意$\mu>0$，每个顶点数为$n$且满足$2s\mid n$、最小半度$\delta^0(D)\geq(\frac{1}{4}+\mu)n$、独立数$\alpha(D)=o(n)$的足够大的有向图$D$，都包含一个$C_{2s}^{\mathrm{ad}}$-因子，该最小半度阈值是渐近紧的。证明过程构建了Ramsey-Turán型格吸收引理，利用叉型结构由小独立条件导出转移。
英文摘要
Let $\overrightarrow{C}$ be any orientation of the cycle $C_{\ell}$ which is not directed. We prove that, for every integer $\ell\ge3$ and every $μ>0$, there is a real $γ$ such that every sufficiently large oriented graph $D$ with $\ell\mid |D|$, minimum semidegree at least $(1/4+μ)|D|$ and independence number at most $γ|D|$ has a $\overrightarrow{C}$-factor. The constant $1/4$ is asymptotically tight. This proof establishes Ramsey-Turán type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.
Comments14pages
