ordered. In an ordered rooted tree $T$, for each node $u\in V(T)$, a *left-to-right* (linear) order $u_1,\dots,u_k$ of the children of $u$ is specified. If $T$ is binary then the first (second) child in the left-to-right order of the children of any node $u$ is the *left* (*right*) *child* of $u$, and the subtree rooted at the left (right) child of $u$ is the *left* (*right*) *subtree* of $u$.

#### Tree drawings.

In a *straight-line drawing* $\Gamma$ of a tree $T$ each node $u$ is represented by a point of the plane (whose coordinates are denoted by $x_{\Gamma}(u)$ and $y_{\Gamma}(u)$) and each edge is represented by a straight-line segment between its end-points. All the drawings considered in this paper are straight-line, even when not specified. In a *planar* drawing no two edges intersect except, possibly, at common end-points. For a rooted tree $T$, a *strictly-upward* drawing $\Gamma$ is such that each edge $(u,p(u))\in E(T)$ is represented by a curve monotonically increasing in the $y$-direction from $u$ to $p(u)$; if $\Gamma$ is a straight-line drawing, this is equivalent to requiring that $y_{\Gamma}(u)<y_{\Gamma}(p(u))$. For an ordered tree $T$, an *order-preserving* drawing $\Gamma$ is such that, for each node $u\in V(T)$, the counter-clockwise 