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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
##### Keywords:
circuit double cover; hypohamiltonian cubic graphs
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##### References:
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