Lower-bound conjecture for plane star-forest decompositions of complete geometric graphs

A complete geometric graph is a complete graph drawn with vertices in general position and straight-line edges. A plane star-forest is a forest whose connected components are stars. Star-forest decomposition lower-bound conjecture. Let $n\ge1$. There is no complete geometric graph with $n$ vertices that can be decomposed into fewer than

$$\left\lceil\frac{3n}{4}\right\rceil$$

plane star-forests. The source presents this as a conjecture based on the lower bound known for vertices in convex position; its general case remains open.