Algorithmic methods of finite discrete structures. Topological graph drawing (part I)
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916341474131968 |
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| author | Kurapov, Sergey Davidovsky, Maxim |
| author_facet | Kurapov, Sergey Davidovsky, Maxim |
| contents | Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing the planarization process by algebraic methods, without making any geometric constructions on the plane. Constructing a rotation of graph vertices solves two most important problems of graph theory simultaneously: the problem of testing a graph for planarity and the problem of constructing a topological drawing of a planar graph. It is shown that the problem of constructing a drawing of a non-planar graph can be reduced to the problem of constructing a drawing of a planar graph, taking into account the introduction of additional vertices characterizing the intersection of edges. Naturally, the development of such a mathematical structure will make it possible to solve the following important problems of graph theory: testing the planarity of a graph, identifying the largest planar subgraph of a graph, determining the thickness of a graph, obtaining a graph with a minimum number of intersections, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithmic methods of finite discrete structures. Topological graph drawing (part I) Kurapov, Sergey Davidovsky, Maxim Combinatorics Discrete Mathematics Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing the planarization process by algebraic methods, without making any geometric constructions on the plane. Constructing a rotation of graph vertices solves two most important problems of graph theory simultaneously: the problem of testing a graph for planarity and the problem of constructing a topological drawing of a planar graph. It is shown that the problem of constructing a drawing of a non-planar graph can be reduced to the problem of constructing a drawing of a planar graph, taking into account the introduction of additional vertices characterizing the intersection of edges. Naturally, the development of such a mathematical structure will make it possible to solve the following important problems of graph theory: testing the planarity of a graph, identifying the largest planar subgraph of a graph, determining the thickness of a graph, obtaining a graph with a minimum number of intersections, etc. |
| title | Algorithmic methods of finite discrete structures. Topological graph drawing (part I) |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2407.21564 |