MathDB

There are

n > 2022

cities in the country. Some pairs of cities are connected with straight two-ways airlines. Call the set of the cities {\it unlucky}, if it is impossible to color the airlines between them in two colors without monochromatic triangle (i.e. three cities

A

B

C

with the airlines

AB

AC

and

BC

of the same color).
The set containing all the cities is unlucky. Is there always an unlucky set containing exactly 2022 cities?

Problem Statement