Ore-type degree condition of supereulerian digraphs

A digraph D is supereulerian if D has a spanning directed eulerian subdigraph. Hong et al. proved that δ+(D)+δ−(D)≥|V(D)|−4 implies D is supereulerian except some well-characterized digraph classes if the minimum degree is large enough. In this paper, we characterize the digraphs D which are not supereulerian under the condition dD+(u)+dD−(v)≥|V(D)|−4 for any pair of vertices u and v with uv∉A(D) without the minimum degree constraint.