graph theory conventions, difference between a PATH and a GRAPH? Consider this example, I did my pseudocode in python

findCycle(G):
    for each edge e in E(G):
        if isThereCycle(G-e):
            G = G - e
    return G 


assume isthereCycle returns whether the graph $G$ has a cycle. 

Input is a graph $G$ that contains a cycle, and the function should return a path of that cycle.

We go through each edge then remove it and see if a cycle still exists without that edge, until we are left with a graph with a single path that is a cycle. (Assume removing the edge (G - e) doesn't mutate the graph unless we do G = G - e).

I want to return a path. Is what I'm returning a path?
Your algorithm returns a cycle rather than a path.

Here is a cycle:



Here is a path:



(Both images taken from Wikipedia.)

To get a path from the cycle, simply remove one edge (this is my best guess for what return a path of that cycle means).

Let me also mention that your algorithm is very inefficient. A much better choice is to use BFS/DFS.