Geodesic
On Decomposing the Complete Symmetric Digraph into Orientations of K4 − e
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 815-828

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Let D be any of the 10 digraphs obtained by orienting the edges of K_4 − e. We establish necessary and sufficient conditions for the existence of a (K_n^*, D)-design for 8 of these digraphs. Partial results as well as some nonexistence results are established for the remaining 2 digraphs.
Keywords: digraph decompositions, orientations of K 4 − e 
@article{DMGT_2019_39_4_a3,
     author = {Bunge, Ryan C. and Darrow, Brian D. and Dubczuk, Toni M. and El-Zanati, Saad I. and Hao, Hanson H. and Keller, Gregory L. and Newkirk, Genevieve A. and Roberts, Dan P.},
     title = {On {Decomposing} the {Complete} {Symmetric} {Digraph} into {Orientations} of {K\protect\textsubscript{4}} \ensuremath{-} e},
     journal = {Discussiones Mathematicae. Graph Theory},
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}
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Bunge, Ryan C.; Darrow, Brian D.; Dubczuk, Toni M.; El-Zanati, Saad I.; Hao, Hanson H.; Keller, Gregory L.; Newkirk, Genevieve A.; Roberts, Dan P. On Decomposing the Complete Symmetric Digraph into Orientations of K4 − e. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 815-828. http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a3/