trail; route system; path
The well known types of routes in graphs and directed graphs, such as walks, trails, paths, and induced paths, are characterized using axioms on vertex sequences. Thus non-graphic characterizations of the various types of routes are obtained.
 L. Nebeský: Route systems and bipartite graphs
. Czechoslovak Math. J. 41 (1991), 260–264. MR 1105440
 L. Nebeský: Route systems of a connected graph
. Math. Bohem. 119 (1994), 407–414. MR 1316593
 L. Nebeský: Characterization of the set of all shortest paths in a connected graph
. Math. Bohem. 119 (1994), 15–20. MR 1303548