Question 115
A convex $2009$-gon is given.
a) Find the maximal number of vertices of this polygon which can be marked in such a way that there are no two marked vertices connected by the side of the polygon.
b) Find the maximal number of vertices of this polygon which can be marked in such a way that among any three of marked vertices there exists at least one which is not connected by the side of the polygon with any of the two others.
a) Find the maximal number of vertices of this polygon which can be marked in such a way that there are no two marked vertices connected by the side of the polygon.
b) Find the maximal number of vertices of this polygon which can be marked in such a way that among any three of marked vertices there exists at least one which is not connected by the side of the polygon with any of the two others.