Problem

Source: Bundeswettbewerb Mathematik 2021, Round 2 - Problem 2

Tags: combinatorics, combinatorics proposed, graph theory, graph cycles



A school has 2021 students, each of which knows at least 45 of the other students (where "knowing" is mutual). Show that there are four students who can be seated at a round table such that each of them knows both of her neighbours.