On some third parts of nearly complete digraphs (Q1970585)

The authors proceed with their investigation of third and near-third parts of complete digraphs [see Combinatorica 18, No.~3, 413-424 (1998; Zbl 0924.05052)]. Neat new results concerning mainly the complete digraphs with \(5\) and with \(9+6k\), \(k\in\{0,1,\dots \}\) vertices are presented. Also an outline of an algorithm to find the \(t\)th parts of a digraph is included. Parts are asked to be self-converse or to have (or not to have) a couple of symmetric arcs. The backtracking method is applied.