edges of a polyhedron are painted with red or yellow
Source: China TST 1991, problem 6
June 27, 2005
inequalitiesgeometry3D geometrytetrahedroncombinatorics unsolvedcombinatoricsgraph theory
Problem Statement
All edges of a polyhedron are painted with red or yellow. For an angle of a facet, if the edges determining it are of different colors, then the angle is called excentric. The excentricity of a vertex , namely , is defined as the number of excentric angles it has. Prove that there exist two vertices and such that .