Abstract. Let [Formula: see text] denote the maximum number of edges not contained in any monochromatic copy of [Formula: see text] in a [Formula: see text]-coloring of the edges of [Formula: see text], and let [Formula: see text] denote the Turán number of [Formula: see text]. In place of [Formula: see text] we simply write [Formula: see text]. Keevash and Sudakov proved that [Formula: see text] if [Formula: see text] is an edge-critical graph or [Formula: see text] and asked if this equality holds for any graph [Formula: see text]. All known exact values of this question require [Formula: see text] to contain at least one cycle. In this paper we focus on acyclic graphs and present the following results: (1) We prove [Formula: see text] when [Formula: see text] is a spider or a double broom. (2) We show that a tail in [Formula: see text] is a path [Formula: see text] such that [Formula: see text] is only adjacent to [Formula: see text], and [Formula: see text] is only adjacent to [Formula: see text] in [Formula: see text]. We obtain a tight upper bound for [Formula: see text] when [Formula: see text] is a bipartite graph with a tail. This result provides the first bipartite graphs which answer the question of Keevash and Sudakov in the negative. (3) We answer a question of Liu, Pikhurko, and Sharifzadeh who asked if [Formula: see text] when [Formula: see text] is a tree. We provide an upper bound for [Formula: see text] and show it is tight when [Formula: see text] is prime. This provides a negative answer to their question.