Torsoids in Path-Like Graphs without nontrivial even 2-separation

Bowler et al. introduced the concept of torsoids that describes the 1-separations of a directed graph in a canonical way building on previous progress by Lov{\'a}sz. To fully understand the structure of directed graphs with respect to their 1-separations it remains to find a global structure along which the torsoids are arranged. In this paper, we start the investigation of this global structure for a specific class of directed graphs.