  There is an old conjecture by Shermer \cite{sher} that in a polygon with $n$
vertices and $h$ holes, $\lfloor \dfrac{n+h}{3} \rfloor$ vertex guards are
sufficient to guard the entire polygon. The conjecture is proved for $h=1$ by
Shermer \cite{sher} and Aggarwal \cite{aga} seperately.
  In this paper, we prove a theorem similar to the Shermer's conjecture for a
special case where the goal is to guard the vertices of the polygon (not the
entire polygon) which is equivalent to finding a dominating set for the
visibility graph of the polygon. Our proof also guarantees that the selected
vertex guards also cover the entire outer boundary (outer perimeter of the
polygon) as well.
