Skip to main content
SpringerLink
Log in

Construction of a Topological Drawing of the Most Planar Subgraph of the Non-planar Graph

  • Linear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

An algorithm was presented to construct a flat drawing of the non-planar graph. The source for solution of the problem is a set of isometric cycles of the graph, which allows one to reduce the solution to the discrete optimization methods. Consideration was given to the necessary concepts and structures for solution of the problem of constructing a planar topological graph drawing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kurapov, S.V. and Tolok, A.V., The Topological Drawing of a Graph. Construction Methods, Autom. Remote Control, 2013, vol. 74, no. 9, pp. 1494–1509.

    Article  MathSciNet  MATH  Google Scholar 

  2. Nishizeki Takao and Rahman Saidur, Planar Graph Drawing, Lect. Notes Ser. Computing., Singapore: World Scientific, 2004, vol. 12.

  3. Garey, M.R. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NP-Completeness, New York: W.H. Freeman, 1979. Translated under the title Vychislitel’nye mashiny i trudnoreshaemye zadachi, Moscow: Mir, 1982.

    MATH  Google Scholar 

  4. Hopcroft, J.E. and Tarjan, R.E., Isomorphism of Planar Graphs, Kibernetich. Sb., 1975, vol. 12, pp. 39–61.

    MATH  Google Scholar 

  5. Reingold, E.M., Nievergelt, J., and Deo, N., Combinatorial Algorithms: Theory and Practice, Englewood Cliffs: Prentice-Hall, 1977. Translated under the title Kombinatornye algoritmy, teoriya i praktika, Moscow: Mir, 1980.

    MATH  Google Scholar 

  6. Kurapov, S.V. and Davidovskii, M.V., Verification for Planarity and Construction of the Topological Drawing of the Planar Graph (by In-depth Search), Prikl. Diskret. Mat., 2016, no. 2 (32), pp. 100–114.

    Google Scholar 

  7. Swamy, M.N.S. and Thulasiraman, K., Graphs, Networks, and Algorithms, New York: Wiley, 1981. Translated under the title Grafy, seti i algoritmy, Moscow: Mir, 1984.

    MATH  Google Scholar 

  8. Ringel, G., Map Color Theorem, New York: Springer, 1974. Translated under the title Teorema o raskraske kart, Moscow: Mir, 1977.

    Book  MATH  Google Scholar 

  9. Kurapov, S.V. and Davidovskii, M.V., Visualization of the Graph of Electrical Circuit Diagram. Geometrical and Topological Drawing of Planar Graph, Kompon. Tekhnol., 2017, no. 2, pp. 80–87.

    Google Scholar 

  10. Kavitha, T., Liebchen, C., Mehlhorn, K., Dimitrios, M., Romeo Rizzi, Ueckerdt, T., and Katharina, A., Cycle Bases in Graphs Characterization, Algorithms, Complexity, and Applications, Comput. Sci. Rev., 2009, vol. 3, pp. 199–243.

    Article  MATH  Google Scholar 

  11. Kurapov, S.V. and Kondrat’eva, N.A., Graph Planarity Algorithms, Visn. Zaporiz. Derzhavn. Univ., Zb. Nauk. Statei. Fiz.-Mat. Nauki, 2001, no. 1, pp. 44–54.

    Google Scholar 

  12. MacLane, S., A Combinatorial Condition for Planar Graphs, Kibernetich. Sb., 1970, vol. 7, pp. 133–144.

    MATH  Google Scholar 

  13. Kozin, I.V., Kurapov, S.V., and Polyuga, S.I., Evolution-Fragmentary Algorithm to Find the Most Planar Sugraph, Prikl. Diskr. Mat., 2015, no. 3 (9), pp. 74–82.

    Google Scholar 

  14. Bellert, S. and Wózniacki, H., The Analysis and Synthesis of Electrical Systems by Means of the Method of Structural Numbers, Warszawa: WNT, 1968. Translated under the title Analiz i sintez elektricheskikh tsepei metodom strukturnykh chisel, Moscow: Mir, 1972.

    Google Scholar 

  15. Lipski, W., Kombinatoryka dla programistow, Warszawa: Wydawnistwa Naukowo–Techniczne, 1982. Translated under the title Kombinatorika dlya programmistov (Combinatorics for Programmers), Moscow: Mir, 1988.

    Google Scholar 

  16. Sergienko, I.V. and Kaspshitskaya, M.F., Modeli i metody resheniya na EVM kombinatornykh zadach optimizatsii (Models and Methods of Computer-aided Solution of Combinatorial Optimization Problems), Kiev: Naukova Dumka, 1981.

    MATH  Google Scholar 

  17. Zykov, A., Osnovy teorii grafov (Fundamentals of the Graph Theory), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  18. Harary, F., Graph Theory, Reading: Addison-Wesley, 1969. Translated under the title Teoriya grafov, Moscow: Mir, 1973.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zaporozhé National University, Zaporozhé, Ukraine

    S. V. Kurapov

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. V. Tolok

Authors
  1. S. V. Kurapov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Tolok
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Kurapov.

Additional information

Original Russian Text © S.V. Kurapov, A.V. Tolok, 2018, published in Avtomatika i Telemekhanika, 2018, No. 5, pp. 24–45.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kurapov, S.V., Tolok, A.V. Construction of a Topological Drawing of the Most Planar Subgraph of the Non-planar Graph. Autom Remote Control 79, 793–810 (2018). https://doi.org/10.1134/S0005117918050028

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117918050028

Keywords

Search

Navigation