CODEWITHSUNDEEP
algorithmgraph-theory
YXD
YXD

Reputation: 32511

Finding all cycles in an undirected graph

If I have an undirected graph, how can I get a list of all cycles?

For example, from the following graph, I would want the cycles:

(a,b,d,e,c)
(a,b,c)
(b,d,e)

enter image description here

Upvotes: 10

Views: 15076

Answers (2)

Akk
Akk

Reputation: 81

this is not possible in polynomial time as if possible then we could use this to find all cycles and hence cycle of largest length which implies we can solve hamiltonian cycle problem completely in polynomial time.

Upvotes: 8

Keith Randall
Keith Randall

Reputation: 23265

You presumably want only simple cycles (those that don't repeat a vertex), or there's an infinite number of them. Even then, there can be an exponential number of cycles. Perhaps this isn't the problem you really want to solve?

Upvotes: 2

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