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Found problems: 1

2019 OMMock - Mexico National Olympiad Mock Exam, 5
Tags: friendly , graph theory , combinatorics
There are $n\geq 2$ people at a party. Each person has at least one friend inside the party. Show that it is possible to choose a group of no more than $\frac{n}{2}$ people at the party, such that any other person outside the group has a friend inside it.