The dominated-or-dominating pair degree-sum conjecture for supereulerian digraphs

Let $D$ be a strong digraph with $n$ vertices. A pair is dominated or dominating when it is a pair of dominated or dominating nonadjacent vertices of $D$ as specified in the source. A digraph is supereulerian if it contains a closed ditrail spanning all vertices, equivalently, a spanning eulerian subdigraph. The dominated-or-dominating pair degree-sum conjecture. If for any pair of dominated or dominating nonadjacent vertices $\{u,v\}$ of $D$,

$$d(u)+d(v)\geq 2n-3,$$

then $D$ is supereulerian. This is presented as a possible generalization of the known degree-sum theorem for all nonadjacent pairs, and its resolution is not given in the supplied text.