(untitled) (Communications in Mathematical Research, 2019)
In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ∂-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ∂-reducible 3-manifold M with one boundary component F of genus n > 0 which admits a complete surface system S′ , if D is a collection of pairwise disjoint compression disks for ∂M, then there exists a complete surface system S for M, which is equivalent to S′ , such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S3.