Regular polygon coloring!
Source: Bulgaria 1998 Problem 6
January 25, 2015
combinatorics proposedcombinatorics
Problem Statement
The sides and diagonals of a regular -gon are colored in colors so that:
(i) For each color and any two vertices , of , the segment is of color or there is a vertex such that and are of color .
(ii) The sides of any triangle with vertices at vertices of are colored in at most two colors.
Prove that .