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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?

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  • $\begingroup$ You return a graph without a cycle which is a forest. If $G$ is a forest in the very beginning, you would return it. $\endgroup$ – Eugene Jul 21 at 23:20
  • $\begingroup$ How am I returning a graph without a cycle when I only remove edges that don't effect the cycle?(Assuming G does have a cycle) $\endgroup$ – Tree Garen Jul 21 at 23:23
  • $\begingroup$ The question was if you return a path. The answer is no. Why? Because if the input is a forest, it is returned unmodified. I am not sure if there are more questions. $\endgroup$ – Eugene Jul 21 at 23:37
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Your algorithm returns a cycle rather than a path.

Here is a cycle:

cycle

Here is a path:

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.

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