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Oleksandr Pryshliak

Publications and source records attributed to Oleksandr Pryshliak.

4 recordsLinked to original sources
arXiv2024

Optimal Reeb graphs on two- and three-connected planar polygon

To investigate the topological structure of planar polygon decomposition on trapezoids, which is formed by height functions. We use the oriented Reeb graph of the function with a marked vertex. We describe all possible optimal Reeb graphs in the case of polygon in general position with one local minimum and one local maximum. By optimal Reeb graph we mean Reeb graph, which cann't be obtaned from other Reeb graph by subdivision of an edge or a leaf attaching. In this case polygon is a triangle with triangle holes. Constructed Reeb graphs give topological structures of trapezoid maps on two-connected polygon with six vertexes and three-connected polygon with nine vertexes.

math.GT↗
arXiv2024

Regular octagons in Poincare model of Lobachevsky geometry

To investigate the topological structure of Morse flows on the 2-disk we use the planar graphs as destinguished graph of the flow. We assume, that the flow is transversal to the boundary of the 2-disk. We give a list of all planar graph with at least 3 edges and describe all planar graphs with 4 edges. We use a list of spherical graph with at least 4 edges.

math.GT↗
arXiv2023

Planar graphs as distinguished graph of Morse flows on the 2-disk

To investigate the topological structure of Morse flows on the 2-disk we use the planar graphs as destinguished graph of the flow. We assume, that the flow is transversal to the boundary of the 2-disk. We give a list of all planar graph with at least 3 edges and describe all planar graphs with 4 edges. We use a list of spherical graph with at least 4 edges.

math.CO↗