Ramsey--Tur\'an Factors of Non-directed Oriented Cycles in Oriented Graphs

Abstract

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 $\mu>0$, there is a real $\gamma$ such that every sufficiently large oriented graph $D$ with $\ell\mid |D|$, minimum semidegree at least $(1/4+\mu)|D|$ and independence number at most $\gamma |D|$ has a $\overrightarrow{C}$-factor. The constant $1/4$ is asymptotically tight. This proof establishes Ramsey-Tur\'an type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.