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Erasing diagonals in an n-gon

Source: Kürschák 1994, problem 2

July 19, 2014
combinatorics unsolvedcombinatorics

Problem Statement

Prove that if we erase n−3n-3 diagonals of a regular nn-gon, then we may still choose n−3n-3 of the remaining diagonals such that they don't intersect inside the nn-gon; but it is possible to erase n−2n-2 diagonals such that this statement doesn't hold.
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