Euler Circuits and Paths

The following are examples of mistakes that should give you an idea what types of mistakes I am looking for at each level.  There are a variety of possible errors while solving problems like this, so this is not an exhaustive list.

As a reminder, here is the scale that is used in class to determine your ability level for each topic:

Below you can randomize problems related to identifying Euler circuits and paths.  You can drag the vertices to clear up some edges if you like.  Reveal the answer with the "Check Answers" button.  The result will only display whether there is a path, circuit, or neither present.  You will still need to identify a correct circuit/path if one exists.