Let X and Y be two sets of points in the plane and M be a set of segments connecting points from X and Y . Let k be a natural number. Prove that the segments from M can be painted using k colors in such a way that for any point x∈X∪Y and two colors α and β (α=β), the difference between the number of α-colored segments and the number of β-colored segments originating in X is less than or equal to 1. graph theorycombinatoricsExtremal combinatoricsExtremal Graph TheoryColoringIMO ShortlistIMO Longlist