Listing all possible train routes I'm interested whether there is the standard solution to the following problem.
Some number of train routes is given:

Route1: First City -> Next City -> ... -> Last City

Route2: ...

...

We need to list all possible ways to get from one given city to the other with possible transfers but without visiting any city more than once. So, for example, if we're given

R1: A -> B -> C

R2: B -> D -> E

R3: C -> D -> A

R4: C -> E -> F

than the routes from A to E are the following:

A -> [R1] -> B -> [R2] -> E

A -> [R1] -> C -> [R4] -> E

I hope i've managed to explain properly. And thank you very much in advance for any tips.
Based on your comments, I'm assuming that if the problem asked to find all paths between $A$ and $B$ on a directed graph, you'd have no problem.  So the only hurdle is how to deal with the extra route information.
Here's an outline of the most obvious approach that I can see:


Convert the given set of routes to an adjacency matrix. Since each edge $(A,B)$ belongs to some route $R$, store that route in the corresponding entry for $(A,B)$ in the matrix.
Run your algorithm to find all paths between your start and goal nodes.
Convert the output of your algorithm to the desired form by collapsing all consecutive edges that belong to the same route into one edge.