Nocycleland is a country with 500 cities and 2013 two-way roads, each one of them connecting two cities. A city A neighbors B if there is one road that connects them, and a city A quasi-neighbors B if there is a city C such that A neighbors C and C neighbors B.
It is known that in Nocycleland, there are no pair of cities connected directly with more than one road, and there are no four cities A, B, C and D such that A neighbors B, B neighbors C, C neighbors D, and D neighbors A.
Show that there is at least one city that quasi-neighbors at least 57 other cities. combinatorics proposedcombinatorics