Pach–Saghafian–Schnider lower-bound conjecture for plane star-forest decompositions

A complete geometric graph is a complete graph drawn with vertices in general position and straight-line edges. A plane $k$-star-forest is a star-forest with at most $k$ connected components. Pach–Saghafian–Schnider's conjecture. The number of plane $k$-star-forests needed to decompose a complete geometric graph on $n$ vertices is at least

$$\frac{(k+1)n}{2k}.$$

This conjecture concerns the variant in which each star-forest is required to have at most $k$ components; the source gives no resolution, so the lower bound remains open.