Question 1
A country has $n\ge2$ cities. Every pair is joined by a direct two-way air route. Licences for these routes are to be given to airlines subject to:
(i) Each route is licensed to exactly one airline.
(ii) Using routes of any one airline, one can travel from any city to every other city.
What is the greatest possible number of airlines?
(i) Each route is licensed to exactly one airline.
(ii) Using routes of any one airline, one can travel from any city to every other city.
What is the greatest possible number of airlines?