IMO 1992 LL FRG20

Let X and Y be two sets of points in the plane and M be a set

imolonglistmathematicsolympiad

IMO 1992 LL FRG20

Origin: FRG

Problem

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 \inX \cupY and two colors \alpha and \beta (\alpha ̸= \beta), the difference between the number of \alpha-colored segments and the number of \beta-colored segments originating in X is less than or equal to 1.