Geodesic
Optimal Eulerian modification of digraphs by addition of arcs
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 1, pp. 102-109

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Тhe following problem is solved: given a directed graph, it is necessary to add to it a minimal number of arcs to obtain an Eulerian directed graph. 
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     author = {A. V. Gavrikov},
     title = {Optimal {Eulerian} modification of digraphs by addition of arcs},
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A. V. Gavrikov. Optimal Eulerian modification of digraphs by addition of arcs. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 1, pp. 102-109. http://geodesic.mathdoc.fr/item/ISU_2012_12_1_a14/