On the structure of the planar subgraphs of obstruction graphs of a nonorientable surface with a given genus-Reference-Cited by-同舟云学术

On the structure of the planar subgraphs of obstruction graphs of a nonorientable surface with a given genus

Published:2021-09-04 Issue:33 Volume: Page:105-109
ISSN:1816-1545
Container-title:Physico-mathematical modelling and informational technologies
language:
Short-container-title:Fìz.-mat. model. ìnf. tehnol.

Author:

Petrenyuk Volodymyr¹

Affiliation:

1. Central Ukrainian National Technical University

Abstract

The problem of studying the structure of planar graphs with sets of points, which should be critical concerning the distance between cells on the boundaries of which the elements of a given set are located in operations of removing vertices or edges of a graph, is considered. Knowing the structure of these planar graphs, it is possible to construct a finite set of planar graphs with given characteristics required for the construction of obstruction graphs of a given nonorientable genus. The main result is to use the constructed list of plane graphs critical concerning distance 2 to construct obstruction graphs of a given nonorientable genus.

Publisher

National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka) (Publications)

Reference5 articles.

1. Khomenko, М. P. (1973). φ - transformation of graphs, preprint IM AHU, Kiev. (in Ukrainian).

2. Khomenko, М. P. (1970). Topological aspects of graph theory, preprint IM AHU, Kiev. (in Russian).

3. Mohar, B., Thomassen, C. (2001). Graphs on Surfaces, Johns Hopkins University Press.

4. Hur, S. (2008). Тhe Кuratowski covering conjecture for graphs of the order less than 10. PhD, Ohio State University.

5. Archdeacon, D., Huneke, P., Kuratowski, A. (1989). Theorem for Nonorientable Surfaces, Journal of combinatorial theory, Series, 46, 173-231.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Models of Klein Surface Obstruction Graphs;Cybernetics and Computer Technologies;2024-03-29

2. On the algorithm for constructing 2-connected minors of the Klein surface;Physico-Mathematical Modelling and Informational Technologies;2023-07-01

3. Structure of Projective Planar Subgraphs of the Graph Obstructions for Fixed Surface;Cybernetics and Computer Technologies;2022-09-30