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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

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CiteScore 2016: 0.16

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Volume 28, Issue 4


A method of graph reduction and its applications

Dmitrii V. Sirotkin
  • Corresponding author
  • National Research University Higher School of Economics, University of Nizhni Novgorod, Nizhni Novgorod, Russia
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/ Dmitriy S. Malyshev
Published Online: 2018-08-16 | DOI: https://doi.org/10.1515/dma-2018-0022


The independent set problem for a given simple graph is to determine the size of a maximal 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

Originally published in Diskretnaya Matematika (2016) 28, №4, 114–125 (in Russian).


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About the article

Received: 2016-12-16

Accepted: 2017-06-01

Published Online: 2018-08-16

Published in Print: 2018-08-28

Citation Information: Discrete Mathematics and Applications, Volume 28, Issue 4, Pages 249–258, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2018-0022.

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