Generalized LR-drawings of trees

TL;DR

This paper extends the LR-drawing method, originally for binary trees, to trees of higher arity by proving the existence of special root-to-leaf paths and using them for generalized drawings.

Contribution

It introduces a generalized LR-drawing technique applicable to trees of arbitrary arity, building on existing binary tree methods.

Findings

Existence of special root-to-leaf paths in higher arity trees

Generalized LR-drawings for arbitrary arity trees

Method preserves properties of original LR-drawings

Abstract

The LR-drawing-method is a method of drawing an ordered rooted binary tree based on drawing one root-to-leaf path on a vertical line and attaching recursively obtained drawings of the subtrees on the left and right. In this paper, we study how to generalize this drawing-method to trees of higher arity. We first prove that (with some careful modifications) the proof of existence of a special root-to-leaf path transfers to trees of higher arity. Then we use such paths to obtain generalized LR-drawings of trees of arbitrary arity.