Ramsey-Tur\'an Anti-Directed Cycle Factors in Oriented Graphs

Abstract

Let $C_{2s}^{\mathrm{ad}}$ be the anti-directed cycle of length $2s$, where $s\geq2$. We prove that, for every $\mu>0$, every sufficiently large $n$-vertex oriented graph $D$ with $2s\mid n$, \[ \delta^0(D)\geq\left(\frac14+\mu\right)n \qquad\text{and}\qquad \alpha(D)=o(n) \] contains a $C_{2s}^{\mathrm{ad}}$-factor. The minimum semidegree threshold is asymptotically tight. The proof develops Ramsey--Tur\'an-type lattice-absorption lemmas with a transferral arising from the small-independence condition by virtue of a fork-type structure.