Addendum to Vertex adjacencies in the set covering polyhedron

Abstract

We study the relationship between the vertices of an up-monotone polyhedron $R$ and those of the polytope $P$ obtained by truncating $R$ with the unit hypercube. When $R$ has binary vertices, we characterize the vertices of $P$ in terms of the vertices of $R$, show their integrality, and prove that the 1-skeleton of $R$ is an induced subgraph of the 1-skeleton of $P$. We conclude by applying our findings to settle a claim in the original paper.