Some Degree Conditions on triple vertices for Digraph to be Supereulerian

Abstract

A digraph D is supereulerian if D has a spanning eulerian subdigraph. We prove that a strong digraph D of order n ≥ 4 satisfies the following conditions: for every triple x, y, z ∊ V(D) such that x and y are non-adjacent, if there is no arc from x to z, then d(x) + d(y) + d⁺(x) + d‾(z) ≥ 3n - 5. Then D is supereulerian.