Bipartite-coloring approximation conjecture for planar MAX-EMST-ratio

Let $P\subseteq\mathbb{R}^2$ be a finite point set. A bipartite coloring is obtained by choosing a Euclidean minimum spanning tree of $P$ and partitioning $P=R\cup B$ so that every edge of the chosen tree has endpoints of different colors. Bipartite-coloring approximation conjecture. For every point set in $\mathbb{R}^2$, the EMST-ratio for any bipartite coloring is a $(1.5)$-approximation for the maximum EMST-ratio.

The source presents triangular chains as examples whose approximation proportion approaches $1.5$, and notes that proving this conjecture would yield an $O(n\log n)$-time $(1.5)$-approximation algorithm for the planar problem.