  An obstacle representation of a graph G is a set of points on the plane
together with a set of polygonal obstacles that determine a visibility graph
isomorphic to G. The obstacle number of G is the minimum number of obstacles
over all obstacle representations of G. Alpert, Koch, and Laison gave a
12-vertex bipartite graph and proved that its obstacle number is two. We show
that a 10-vertex induced subgraph of this graph has obstacle number two. Alpert
et al. also constructed very large graphs with vertex set consisting of a
clique and an independent set in order to show that obstacle number is an
unbounded parameter. We specify a 70-vertex graph with vertex set consisting of
a clique and an independent set, and prove that it has obstacle number greater
than one. This is an ancillary document to our article in press. We conclude by
showing that a 10-vertex graph with vertex set consisting of two cliques has
obstacle number greater than one, improving on a result therein.
