TITLE: Hidden points in polygons
QUESTION [20 upvotes]: Let $h(n)$ be the largest number of mutually invisible points that can be located in a
polygon $P$ of $n$ vertices. Two points $x$ and $y$ are mutually invisible if the segment
$xy$ contains a point strictly exterior to the closed set $P$.
   
I have a vague sense that this question—What is $h(n)$?—may have been studied before, and perhaps even entirely resolved, but I am not recalling references. Any help would be appreciated—Thanks!

Answered by Wlodek Kuperberg:
 
The same construction shows that $h(n)=n-3$ for hiding points in a 
polyhedron of $n$ vertices in $\mathbb{R}^3$.

REPLY [14 votes]: OK - following the suggestion of Mariano Suárez-Alvarez, a moderator - I post my comment as an answer:
If k points are mutually invisible in an n-sided poygon, then no two of them lie in the same triangle of a triangulation. Therefore $h(n)≤n−2$, and there is a simple example, generalizing your construction for $n=4$ and $5$, of an $(n+2)$-sided polygon with $n$ mutually invisible points in it, for every $n$: Draw a concave-up arc of a circle tangent to your "V" at its upper ends and place $n$ vertices on it. Place your red points very close to the midpoints of the chords of the circular arc. Unless I misinterpret your question, this shows that $h(n)=n−2\ \ $ for every $n≥3$.