Before revision:  Let f_d(n) denote the minimum number N of points such that every n-vertex tree with maximum degree d\in\{3,4\ admits an L-shaped embedding in every point set of size N, where no two points have the same abscissa or ordinate. The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .
After revision:  Let f_d(n) denote the minimum number N of points such that every n-vertex tree with maximum degree d\in\{3,4\ admits an L-shaped embedding of any n-vertex tree with maximum degree 4. However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .