Abstract
A digraph D is supereulerian if D has a spanning eulerian subdigraph. We investigate forbidden induced subdigraph conditions for a strong digraph to be supereulerian. The subdigraph H is a semi-path in D if its undirected version is a path in G(D). Let SPk denote the semi-path on k vertices. For k = 4, we determine the smallest integer h(k) such that if a strong strict digraph D containing a subdigraph H isomorphic to SPk always satisfies vertical bar A(D [V (H)])vertical bar >= h(k), then D is supereulerian.