The six-point MST-ratio conjecture for planar point sets

Let $P$ be a set of $n$ points in the plane. Write $w(P)$ for the length of a Euclidean minimum spanning tree of $P$, and let

$$\gamma(P)=\max_{P=R\cup B}\frac{w(R)+w(B)}{w(P)},$$

where the maximum is over all non-trivial bipartitions of $P$ into two sets. Six-point MST-ratio conjecture. For any set $P$ of $n\geq 6$ points in the plane, we have $\gamma(P)>1$. This would improve the paper's established guarantee from $n\geq 12$ to $n\geq 6$; the conjecture is presented as an open question in the source.