Supereulerian digraphs with given diameter

A digraph D is supereulerian if D has a spanning eulerian subdigraph. Let diam(D) denote the diameter of D. In this paper, we obtain sufficient conditions on digraph to be supereulerian for given diameter. In particular, we prove that if a digraph D with diam(D) ≤ 2, then D is supereulerian. And for a bipartite digraph D, if diam(D) ≤ 3, then it is supereulerian.