Problem

Source: China Mathematical Olympiad 1990 problem6

Tags: combinatorics unsolved, combinatorics



A convex $n$-gon and its $n-3$ diagonals which have no common point inside the polygon form a subdivision graph. Show that if and only if $3|n$, there exists a subdivision graph that can be drawn in one closed stroke. (i.e. start from a certain vertex, get through every edges and diagonals exactly one time, finally back to the starting vertex.)