Decompositions of complete digraphs into small tripartite digraphs
Necessary and sufficient conditions on n are established for the existence of a (Kn∗, D)-design where D is any digraph obtained by orienting the edges of a triangle with a pendant edge.
Bunge, Ryan C., Camry J. Cowan, Laban J. Cross, Saad I. El-Zanati, Annie E. Hart, D. Roberts, and Asia M. Youngblood. "Decompositions of complete digraphs into small tripartite digraphs." Journal of Combinatorial Mathematics and Combinatorial Computing 102 (2017): 239-251.