ASU 196 All Soviet Union MO 1974 connecting red, blue points
Source:
July 4, 2019
combinatoricsColoring
Problem Statement
Given some red and blue points. Some of them are connected by the segments. Let us call "exclusive" the point, if its colour differs from the colour of more than half of the connected points. Every move one arbitrary "exclusive" point is repainted to the other colour. Prove that after the finite number of moves there will remain no "exclusive" points.