Bundeswettbewerb Mathematik 1987 Problem 2.2
Source: Bundeswettbewerb Mathematik 1987 Round 2
October 12, 2022
polyhedroncombinatoricsDirected graphscycles
Problem Statement
An arrow is assigned to each edge of a polyhedron such that for each vertex, there is an arrow pointing towards that vertex and an arrow pointing away from that vertex. Prove that there exist at least two faces such that the arrows on their boundaries form a cycle.