Algorithmic methods of finite discrete structures. Topological graph drawing (part IV)

TL;DR

This paper introduces mathematical models and methods for creating topological drawings of complex non-planar graphs, utilizing vertex rotation theory and cycle systems to determine optimal embeddings.

Contribution

It develops new models for topological graph drawing based on G. Ringel's vertex rotation theory, including methods for locating imaginary vertices and constructing maximum planar subgraphs.

Findings

A method for topological drawing of non-separable non-planar graphs.

Techniques for locating imaginary vertices via intersection analysis.

Use of maximum planar subgraphs as a basis for drawings.

Abstract

The chapter presents mathematical models intended for creating a topological drawing of a non-separable non-planar graph based on the methods of G. Ringel's vertex rotation theory. The induced system of cycles generates a topological drawing of a certain thickness. A method for determining the location of imaginary vertices by finding the intersection of connections on a plane is presented. A topological drawing of a maximum planar subgraph is used as a basis.