Algorithmic methods of finite discrete structures Topological graph drawing (part I)
<|reference_start|>Algorithmic methods of finite discrete structures Topological graph drawing (part I): 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.<|reference_end|>
@article{kurapov2024algorithmic,
    title={Algorithmic methods of finite discrete structures. Topological graph
  drawing (part I)},
    author={Sergey Kurapov, Maxim Davidovsky},
    journal={arXiv preprint arXiv:2407.21564},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.21564},
    primaryClass={math.CO cs.DM}
}