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Plane increasing trees are rooted labeled trees embedded into the plane suchthat the sequence of labels is increasing on any branch starting at the root.Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. Weconstruct a bijection between these two combinatorial objects and study thetherefrom arising connections of certain parameters. Furthermore, we showcentral limit theorems for two statistics on leaves. We end the study byconsidering more than 20 subclasses and their bijective counterparts. Many ofthese subclasses are enumerated by known counting sequences, and thus enrichtheir combinatorial interpretation.

A bijection of plane increasing trees with relaxed binary trees of right height at most one