Circuit double covers in special types of cubic graphs

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 ∈ V ( G ) ) have strong circuit double covers.