Geodesic
On directed acyclic exact extensions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 83-88

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Exact extensions of undirected graphs are well studied, but exact extensions of directed graphs are much less known.We prove that only directed acyclic graph or strongly connected graph can be an exact extension. Furthermore, only transitive tournament can be directed acyclic exact extension. 
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M. B. Abrosimov; A. A. Dolgov. On directed acyclic exact extensions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 83-88. http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a13/