MathDB
Circular colored graph, minimum of colors needed

Source: Latvian TST for Baltic Way 2022 P7

November 25, 2022
combinatoricsgraph theory

Problem Statement

A kingdom has 20212021 towns. All of the towns lie on a circle, and there is a one-way road going from every town to the next 101101 towns in a clockwise order. Each road is colored in one color. Additionally, it is known that for any ordered pair of towns AA and BB it is possible to find a path from AA to BB so that no two roads of the path would have the same color. Find the minimal number of road colors in the kingdom.