Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
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.
Cite
@article{arxiv.2506.10936,
title = {Algorithmic methods of finite discrete structures. Topological graph drawing (part III)},
author = {Sergey Kurapov and Maxim Davidovsky},
journal= {arXiv preprint arXiv:2506.10936},
year = {2025}
}
Comments
120 pages, in Ukrainian language, 112 figures, a preprint of monography