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 , proving that f_d(n) = 10 vertices, and we show that every ordered tree on n\leq 9 or n=11 vertices admits an L-shaped embedding in every set of n points. We also construct an infinite family of ordered trees which do not always admit an L-shaped embedding, answering a question raised by Biedl, Chan, Derka, Jain, and Lubiw .