In the plane we are given a set
of 1991 points, and certain pairs of these points are joined with a path. We suppose that for every point of
there exist at least 1593 other points of
to which it is joined by a path. Show that there exist six points of
every pair of which are joined by a path.
Alternative version: Is it possible to find a set
of 1991 points in the plane and paths joining certain pairs of the points in
such that every point of
is joined with a path to at least 1592 other points of
and in every subset of six points of
there exist at least two points that are not joined?
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E,](/media/m/6/8/5/685b3a57f02ee1cb014702dca42252d5.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
Alternative version: Is it possible to find a set
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E,](/media/m/6/8/5/685b3a57f02ee1cb014702dca42252d5.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)