MathDB
Flights distributed to airway companies

Source: Turkey TST 2013 - Day 3 - P3

April 2, 2013
inductiongraph theorycombinatorics proposedcombinatorics

Problem Statement

Some cities of a country consisting of nn cities are connected by round trip flights so that there are at least kk flights from any city and any city is reachable from any city. Prove that for any such flight organization these flights can be distributed among nāˆ’kn-k air companies so that one can reach any city from any city by using of at most one flight of each air company.