Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918057182494720 |
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| author | Kurapov, Sergey Davidovsky, Maxim |
| author_facet | Kurapov, Sergey Davidovsky, Maxim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10936 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algorithmic methods of finite discrete structures. Topological graph drawing (part III) Kurapov, Sergey Davidovsky, Maxim Combinatorics Discrete Mathematics Operator Algebras 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. |
| title | Algorithmic methods of finite discrete structures. Topological graph drawing (part III) |
| topic | Combinatorics Discrete Mathematics Operator Algebras |
| url | https://arxiv.org/abs/2506.10936 |