Noncrossing trees are almost conditioned Galton-Watson trees

Abstract

A noncrossing tree (NC-tree) is a tree drawn on the plane having as vertices a set of points on the boundary of a circle, and whose edges are straight line segments that do not cross. In this article, we show that NC-trees with size n are conditioned Galton-Watson trees. As corollaries, we give the limit law of depth-first traversal processes and the limit profile of NC-trees.