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TOT 201 1988 Autumn S4 1988 towns and 4000 roads

Source:

March 7, 2021
combinatorics

Problem Statement

There are 19881988 towns and 40004000 roads in a certain country (each road connects two towns) . Prove that there is a closed path passing through no more than 2020 towns.
(A. Razborov , Moscow)