Ramsey-Turán Anti-Directed Cycle Factors in Oriented Graphs

Abstract

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

15pages