Simple 2n-gon
Source: Iran TST 2014, second exam, day 2 ,problem 3
January 1, 2015
combinatorics unsolvedcombinatorics
Problem Statement
Consider segments in the plane which no two intersect and between their endpoints no three are collinear. Is the following statement true?
Statement: There exists a simple -gon such that it's vertices are the endpoints of the segments and each segment is either completely inside the polygon or an edge of the polygon.