How to draw combinatorial map? From graphs and edges to corner rotations and permutations

TL;DR

This paper advocates for using corners instead of halfedges in combinatorial maps, establishing a uniform terminology based on rotations, and explores how this approach can improve graph drawing and algorithms.

Contribution

It introduces a corner-based approach to combinatorial maps, emphasizing rotational prevalence for clearer and more natural graph representations.

Findings

Corners are more natural than halfedges for graph drawing.

Rotational prevalence simplifies combinatorial map structures.

The corner approach enhances clarity and conciseness in graph algorithms.

Abstract

In this article we consider combinatorial maps approach to graphs on surfaces, and how between them can be establish terminological uniformity in favor of combinatorial maps in way rotations are set as base structural elements and all other notions are derived from them. We set this approach as rotational prevalence principle. We consider simplest way how to draw combinatorial map, and ask how this approach in form of rotational prevalence could be used in graphs drawing practice and wider in algorithms. We try to show in this paper that the use of corners in the place of halfedges is much more natural than that of halfedges. Formally there is no difference between both choices, but corner approach is much more clear and concise, thus we advocate for that.