# 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?

• You return a graph without a cycle which is a forest. If $G$ is a forest in the very beginning, you would return it. – Eugene Jul 21 '19 at 23:20
• 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) – Tree Garen Jul 21 '19 at 23:23
• 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. – Eugene Jul 21 '19 at 23:37

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.