I think you are on the right track with the figure 8 configuration. I think the two loops are what are important for traversing both directions. I would forma

I think you are on the right track with the figure 8 configuration. I think the two loops are what are important for traversing both directions. I would formally define this loop as follows. (Note: that since these edges are directional I am using "->" to denote these edges.) Definition: Junction Loop Consider an arbitrary junction K with vertices l,m,n such that l->m and l->n. This junction K will contain a loop if there exists a path that connects m->n or n->m. ------------------------------ Defintion: A Dmichulke Track A Dmichulke Track is a track that any piece of track can be traversed in both directions and there exists a path between any two pieces of track ------------------------------- Conjecture: Any track will be a Dmichulke track if it has a two junctions J_1 (with vertices a,b,c such that a->b, a->c) and J_2 ( with vertices x,y,z where x->y and x->z) that satisfy the following conditions. 1) J_1 and J_2 must be have a path connecting vertex a to vertex x 2) J_1 and J_2 must contain a loop. 3) There must exist a path to either of these junctions from any point of the track. ------------------------------- This should satisfy the stated conditions. You should play around with track configurations that satisfy these conditions and see if you can find a counter example. This is only a conjecture though since I didn't really prove anything. I may take a crack at working on that proof over the weekend and let you know how it goes.