MathDB
Nice problem

Source: Tuymaada 2016

June 28, 2017
combinatoricsgraph theory

Problem Statement

The flights map of air company Kr,rK_{r,r} presents several cities. Some cities are connected by a direct (two way) flight, the total number of flights is m. One must choose two non-intersecting groups of r cities each so that every city of the first group is connected by a flight with every city of the second group. Prove that number of possible choices does not exceed 2mr2*m^r .