How Close is a Tree to a Euclidean Minimum Spanning Tree?

Todor Antić, Jiří Fiala, Jelena Glišić +8

Let $\hat{I}“$ be a straight-line crossing-free drawing of a tree $T$. A \emph{bad pair} in $\hat{I}“$ is a pair of non-adjacent vertices of $T$ whose Euclidean distance in $\hat{I}“$ is smaller tha…