Before revision:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points , proving that f_d(n) = n, d\in\{3, 4\ .
After revision:  In this paper, we present the first examples of n-vertex trees for n\in\{13,14,16,17,18,19,20\} that require strictly more points than vertices to admit an L-shaped embedding , proving that f_4(n)\geq n+1 for those n . Moreover, using computer assistance , we show that every tree on n\leq 11 vertices admits an L-shaped embedding in every set of n points . We also consider embedding ordered trees, where the cyclic order of the neighbors of each vertex in the embedding is prescribed. For this setting, we determine the smallest non-embeddable ordered tree on n = n, d\in\{3, 4\ .