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Circuit double covers in special types of cubic graphs. (English) Zbl 1218.05129

Summary: Suppose that a 2-connected cubic graph \(G\) of order \(n\) has a circuit \(C\) of length at least \(n - 4\) such that \(G - V(C)\) is connected. We show that \(G\) has a circuit double cover containing a prescribed set of circuits which satisfy certain conditions. It follows that hypohamiltonian cubic graphs (i.e., non-hamiltonian cubic graphs \(G\) such that \(G - v\) is hamiltonian for every \(v\in V(G))\) have strong circuit double covers.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C40 Connectivity
05C38 Paths and cycles
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