Dominant-Degree Conditions for Ramsey--Turán Factors of Non-Directed Cycle Orientations

Let $\Cvec$ be a fixed orientation of the cycle $C_\ell$, $\ell\ge3$, which is not directed. For an oriented graph $D$, let $d_D^*(v):=\max\{d_D^+(v),d_D^-(v)\},$ and let \[ \sigore(D):=\min\bigl\{d_D^*(x)+d_D^*(y):x\ne y,\ xy,yx\notin A(D)\bigr\}, \] with $\sigore(D)=\infty$ if the underlying gra