Here is my problem which I am trying to solve since one complete year. With no success till end of the year. I have to seek help and a concrete solutions from the stackoverflow
Perhaps you can look into the traveling salesman problem if your still struggling with the above. TSP visits cities only once. And if in your case each node is a crossing for your strike-through then this might help.
Check here for the python code to look at. I've checked and the print statement looks nice and structured. Well done cMinor!
Edit based on discussion: file 1, file2, file3.