Find all chordless cycles in an undirected graph

Question

How to find all chordless cycles in an undirected graph?

For example, given the graph

0 --- 1
|     | \\
|     |  \\
4 --- 3 - 2

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Answer 1

Just a thought:

Let's say you are enumerating cycles on your example graph and you are starting from node 0.

If you do a breadth-first search for each given edge, e.g. 0 - 1, you reach a fork at 1. Then the cycles that reach 0 again first are chordless, and the rest are not and can be eliminated... at least I think this is the case.

Could you use an approach like this? Or is there a counterexample?