Minimal number of inner diagonals iff none of them intersect
Source: MEMO 2015, problem I-2.
August 27, 2015
combinatoricspolygondiagonalscombinatorial geometry
Problem Statement
Let be an integer. An inner diagonal of a simple -gon is a diagonal that is contained in the -gon. Denote by the number of all inner diagonals of a simple -gon and by the least possible value of , where is a simple -gon. Prove that no two inner diagonals of intersect (except possibly at a common endpoint) if and only if .Remark: A simple -gon is a non-self-intersecting polygon with vertices. A polygon is not necessarily convex.