1 % guess the path
   2 path(X,Y) v outPath(X,Y) :- edge(X,Y), reached(X).
   3 :- start(X), path(_,X).
   4 
   5 % each vertex in the path must have at most one
   6 % incoming and one outcoming edge 
   7 :- vtx(X), path(X,Y), path(X,Z), Y != Z.
   8 :- vtx(X), path(X1,X), path(X2,X), X1 != X2.
   9 
  10 % the path must feature all vertices
  11 :- vtx(X), not reached(X).
  12 reached(X) :- path(Y,X).
  13 reached(X) :- start(X).