There are n(n≥8) airports, some of which have one-way direct routes between them. For any two airports a and b, there is at most one one-way direct route from a to b (there may be both one-way direct routes from a to b and from b to a). For any set A composed of airports (1≤∣A∣≤n−1), there are at least 4⋅min{∣A∣,n−∣A∣} one-way direct routes from the airport in A to the airport not in A.
Prove that: For any airport x, we can start from x and return to the airport by no more than 2n one-way direct routes. combinatoricsdirected graphgraph cycles