Problem

Source: 2015 Cuba 1.2

Tags: combinatorics



In a certain country there are 9 cities and two airline companies: AeroSol and AeroLuna. Between each pair of cities there are flights from one and only one of them. the two companies. Furthermore, for any triple of cities $X$, $Y$,$ Z$ σt least one of the flights between them is served by AeroLuna. It is possible to find $4$ cities such that all flights between them be served by AeroLuna?