Kang, Qingde; Liang, Zhihe Optimal packings and coverings of \(\lambda\)DK\(_v\). (English) Zbl 0989.05094 J. Comb. Math. Comb. Comput. 39, 203-253 (2001). Summary: Let \(\lambda\text{DK}_v\) denote the complete directed multigraph with \(v\) vertices, where any two distinct vertices \(x\) and \(y\) are joined by \(\lambda\) arcs \((x, y)\) and \(\lambda\) arcs \((y, x)\). By a \(k\)-circuit we mean a directed cycle of length \(k\). In this paper, we consider the problem of constructing maximal packings and minimal coverings of \(\lambda\text{DK}_v\) with \(k\)-circuits. Using the leave-arcs graph of packing and the repeat-arcs graph of covering, we give a unified method for finding packings and coverings. Also, we completely solve the existence of optimal packings and coverings for \(5\leq k\leq 14\) and any \(\lambda\). Cited in 1 Document MSC: 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05B40 Combinatorial aspects of packing and covering Keywords:decomposition; Mendelsohn design; complete directed multigraph; maximal packings; minimal coverings PDFBibTeX XMLCite \textit{Q. Kang} and \textit{Z. Liang}, J. Comb. Math. Comb. Comput. 39, 203--253 (2001; Zbl 0989.05094)