MathDB

1

Part of 1983 IMO Shortlist

Problems(1)

Airlines

Source:

9/9/2010
The localities P1,P2,…,P1983P_1, P_2, \dots, P_{1983} are served by ten international airlines A1,A2,…,A10A_1,A_2, \dots , A_{10}. It is noticed that there is direct service (without stops) between any two of these localities and that all airline schedules offer round-trip flights. Prove that at least one of the airlines can offer a round trip with an odd number of landings.
combinatoricsExtremal combinatoricsRamsey Theorygraph theoryExtremal Graph TheoryIMO Shortlist