Packings and coverings of the complete directed multigraph with 3- and 4-circuits

AbstractLet λDKv denote the complete directed multigraph with v vertices, where any two distinct vertices x and y are joined by λ arcs (x, y) and λ arcs (y, x). By a k-circuit we mean a directed cycle of length k. In this paper, we consider the problem of finding maximal packings and minimal coverings of λDKv with k-circuits. In particular, we completely determine the packing number and covering number for the cases k = 3 and 4