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Lemma: When is it possible to find a separating cycle in a biconnected graph, given a nonseparating cycle?
Let \(G(V,E,\gamma)\) be a biconnected graph and let \(C(V_c,E_c)\) be a nonseparating cycle with the piece \(P(V_p,E_p)\). If \(P\) is not a path, then it is possible to construct a separating cycle \(S(V_s,E_s)\), which consists of a subpath of \(C\) plus a path of \(P\) between two attachments of \(P\).
Table of Contents
Proofs: 1
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References
Bibliography
 Di Battista G., Eades P., Tamassia R., Tollis, I.G.: "Graph Drawing  Algorithms for the Visualization of Graphs", PrenticeHall, Inc., 1999