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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.

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