MathNet 2016-part-05 — 184 problems (EN–VI) Question 29

Given are $2n-1$ two-element subsets of the set $\{1,2, \ldots, n\}$. Prove that one can choose $n$ of these subsets whose union contains at most $\frac{2}{3}n+1$ elements.

(Dusan Djukic)