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

Find all cycles.

Definition of a chordless cycle is a set of points in which a subset cycle of those points don't exist. So, once you have all cycles problem is simply to eliminate cycles which do have a subset cycle.

For efficiency, for each cycle you find, loop through all existing cycles and verify that it is not a subset of another cycle or vice versa, and if so, eliminate the larger cycle.

Beyond that, only difficulty is figuring out how to write an algorithm that determines if a set is a subset of another.