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Diskr. Mat., 2017, Volume 29, Issue 3, Pages 114–125 (Mi dm1440)  

This article is cited in 1 scientific paper (total in 1 paper)

A method of graph reduction and its applications

D. V. sirotkin, D. S. Malyshev

National Research University – Higher School of Economics in Nizhny Novgorod

Abstract: The independent set problem for a given simple graph is to determine the size of a maximum set of its pairwise non-adjacent vertices. We propose a new way of graph reduction leading to a new proof of the NP-completeness of the independent set problem in the class of planar graphs and to the proof of NP-completeness of this problem in the class of planar graphs having only triangular internal facets of maximal vertex degree 18.

Keywords: independent sets, planar graph, planar triangulation, computational complexity.

Funding Agency Grant Number
Russian Science Foundation 17-11-01336
Исследование выполнено за счет гранта Российского научного фонда (проект № 17-11-01336).


DOI: https://doi.org/10.4213/dm1440

Full text: PDF file (506 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:4, 249–258

Bibliographic databases:

UDC: 519.17
Received: 16.12.2016

Citation: D. V. sirotkin, D. S. Malyshev, “A method of graph reduction and its applications”, Diskr. Mat., 29:3 (2017), 114–125; Discrete Math. Appl., 28:4 (2018), 249–258

Citation in format AMSBIB
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\by D.~V.~sirotkin, D.~S.~Malyshev
\paper A method of graph reduction and its applications
\jour Diskr. Mat.
\yr 2017
\vol 29
\issue 3
\pages 114--125
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\crossref{https://doi.org/10.4213/dm1440}
\elib{http://elibrary.ru/item.asp?id=29887805}
\transl
\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 4
\pages 249--258
\crossref{https://doi.org/10.1515/dma-2018-0022}
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  • http://mi.mathnet.ru/eng/dm1440
  • https://doi.org/10.4213/dm1440
  • http://mi.mathnet.ru/eng/dm/v29/i3/p114

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Sirotkin, D. S. Malyshev, “Konstruktivnaya teorema suschestvovaniya, assotsiirovannaya s lokalnymi preobrazovaniyami grafov dlya zadachi o nezavisimom mnozhestve”, Zhurnal SVMO, 21:2 (2019), 215–221  mathnet  crossref  elib
  • Дискретная математика
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