MathDB
k flights in n cities from 2 airlines

Source: St Petersburg 2019 10.2

May 1, 2019
combinatoricsmaximum

Problem Statement

Every two of the nn cities of Ruritania are connected by a direct flight of one from two airlines. Promonopoly Committee wants at least kk flights performed by one company. To do this, he can at least every day to choose any three cities and change the ownership of the three flights connecting these cities each other (that is, to take each of these flights from a company that performs it, and pass the other). What is the largest kk committee knowingly will be able to achieve its goal in no time, no matter how the flights are distributed hour?