Question 4
In space, $n\ge2$ points are given, no four coplanar, together with $\tfrac12(n^2-3n+4)$ segments whose endpoints are among those points. At least one segment has the following property: after removing it but retaining its endpoints, there are two distinct points which cannot be joined by any polygonal path made of the remaining segments. Find the largest number $k$ for which $k$ of the given segments form a closed polygonal path, each of whose vertices is incident with exactly two segments of that path.
Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.
Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.