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arXiv · 2506.10936

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

Sergey Kurapov·Maxim Davidovsky
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Abstract

The manuscript considers mathematical models for creating a topological drawing of a graph based on the methods of G. Ringel's vertex rotation theory. An algorithm is presented for generating a topological drawing of a flat part of a graph based on the selection of a basis for the cycle subspace C(G) using the Monte Carlo method. A steepest descent method for constructing a topological drawing of a flat subgraph is described in the manuscript. The topological drawing of a graph is constructed using a combination of the methods of vector intersection algebra developed by L. I. Rapport. Three stages of constructing a flat subgraph of a non-separable graph are described. The issues of constructing a Hamiltonian cycle based on constructing a flat subgraph are considered. A new method for constructing a Hamiltonian cycle of a graph based on the cycle graph of a flat subgraph is described.

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Sergey Kurapov, Maxim Davidovsky. 2025-06-12. Algorithmic methods of finite discrete structures. Topological graph drawing (part III). https://arxiv.org/abs/2506.10936

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