  We prove that for any finite tree $T$ with $n$ vertices and maximal degree
$3$, there is a topological embedding of $T$ into the integer grid $Z^2$ which
maps vertices to vertices and whose image meets at most $\frac{7}{3}n$
vertices. This recovers a weaker form of a result due to Valiant
10.5555/1963635.1963641 with stronger constants. We address question $7.7$ of
arXiv:2112.05305, giving the first example of a pair of graphs $X,Y$ such that
there is no regular map $X\to Y$ but the coarse wiring profile of $X$ into $Y$
grows linearly.
