Learning entailment rules is fundamental in many semantic-inference applications and has been an active field of research in recent years. In this paper we address the problem of learning transitive graphs that describe entailment rules between predicates (termed entailment graphs). We first identify that entailment graphs exhibit a "tree-like" property and are very similar to a novel type of graph termed forest-reducible graph. We utilize this property to develop an iterative efficient approximation algorithm for learning the graph edges, where each iteration takes linear time. We compare our approximation algorithm to a recently-proposed state-of-the-art exact algorithm and show that it is more efficient and scalable both theoretically and empirically, while its output quality is close to that given by the optimal solution of the exact algorithm.