On Decomposing the Complete Symmetric Digraph into Orientations of K<sub>4</sub> − e

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.

Geodesic

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On Decomposing the Complete Symmetric Digraph into Orientations of K₄ − e

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.

Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 815-828

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Résumé

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

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     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},
     pages = {815--828},
     publisher = {mathdoc},
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     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a3/}
}

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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/