My son has a wooden train set. It has straight tracks, curves, and points. I've been [strike]playing with it[/strike]building tracks for him, and came across something odd. If I don't really think about it and just throw something together, it almost always seems to end up that there is a "trap" - a section of track that you cannot get back out of without backing up. I am not sure of the correct terminology, so I describe a set of points as a Y with two "arms" and one "leg". Entering from the leg you can choose either arm; entering from either arm you must exit via the leg. For an example of a "trap", consider a set of points with one arm of the Y connected to some network, and the other arm connected to the leg. If you enter the points from the network, you are stuck on the loop unless you back up. I have two questions: 1 - is my experience that networks with traps are more common representative, or am I a klutz? 2 - what do I need to read up on to understand what's going on? I tried enumeration to answer (1), but the number of possible networks gets large fast. There are 2 with no sets of points (a straight line and a loop), 3 with one set of points (an open Y, a loop with a siding, and a return-to-sender), and I think I counted 17 with two sets of points (although I may have been double counting something - even a taxonomy for networks would be helpful!). My son's set has five sets of points... I guess the answer to (2) is graph theory - are there any recommended resources? And is there a particular branch (see what I did there?) that I should be particularly looking at?