Let n and k be arbitrary non-negative integers. Suppose we have drawn 2kn+1 (different) diagonals of a convex n-gon. Show that there exists a broken line formed by 2k+1 of these diagonals that passes through no point more than once. Prove also that this is not necessarily true when we draw only kn diagonals. graph theorycombinatorics unsolvedcombinatorics