Sufficient Ore type condition for a digraph to be supereulerian

Abstract

A digraph D is called supereulerian if D has a spanning eulerian subdigraph. In this article, we show that a strong digraph D with n vertices is supereulerian if for every three different vertices z,w and v such that z and w are nonadjacent, d(z)+d(w)+d+(z)+d−(v)≥3n−5 (if (z,v)∉A(D)) and d(z)+d(w)+d−(z)+d+(v)≥3n−5 (if (v,z)∉A(D)). And this bound is sharp.