Pruning a highly connected graph
Source: Poland 73-3-3
March 31, 2022
combinatorics
Problem Statement
One has marked points on a circle and has drawn a certain number of chords whose endpoints are the marked points. It turned out that the following property is satisfied: whenever any drawn chords are removed one can join any two marked points by a broken line composed of some of the remaining drawn chords. Prove that one can remove some of the drawn chords so that at most chords remain and the property described above is preserved.