Proximity Drawings of High-Degree Trees

TL;DR

This paper investigates how to aesthetically draw high-degree trees by partitioning them into subtrees of bounded degree, ensuring each part is optimally represented, extending previous limitations on maximum degree.

Contribution

It introduces a method to draw high-degree trees by partitioning into subtrees, allowing for aesthetically pleasing drawings beyond degree 6.

Findings

Partitioning trees enables drawing high-degree trees as minimum spanning trees.

Natural properties of partitions guarantee the existence of such drawings.

Extends the class of trees that can be drawn aesthetically beyond degree 6.

Abstract

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the partition or covering satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set.