CMO 1990 Problem 6

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 graphthat 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.)