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On removable even circuits in graphs. (English) Zbl 1053.05074

Discrete Math. 286, No. 3, 177-184 (2004); erratum ibid. 297, 210-213 (2005).
Summary: Let \(G\) be a connected graph with minimum degree at least 3. We prove that there exists an even circuit \(C\) in \(G\) such that \(G-E(C)\) is either connected or contains precisely two components one of which is isomorphic to a 1-bond. We further prove sufficient conditions for there to exist an even circuit \(C\) in a 2-connected simple graph \(G\) such that \(G-E(C)\) is 2-connected. As a consequence of this, we obtain sufficient conditions for there to exist an even circuit \(C\) in a 2-connected graph \(G\) for which \(G-E(C)\) is 2-connected.

MSC:

05C38 Paths and cycles
05C40 Connectivity
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References:

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