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Expanding operators for the independent set problem

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Abstract

The notion is introduced of an expanding operator for the independent set problem. This notion is a useful tool for the constructive formation of new cases with the efficient solvability of this problem in the family of hereditary classes of graphs and is applied to hereditary parts of the set Free({P 5, C 5}). It is proved that if for a connected graph G the problem is polynomial-time solvable in the class Free({P 5, C 5,G}) then it remains so in the class Free({P 5, C 5,G ○ \(\bar K_2 \), G ⊕ K 1,p ) for every p. We also find two new hereditary subsets of Free({P 5, C 5}) with polynomially solvable independent set problem that are not a corollary of applying the revealed operators.

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Authors and Affiliations

  1. National Research University Higher School of Economics at Nizhni Novgorod, B. Pecherskaya ul. 25/12, Nizhni Novgorod, 603155, Russia

    D. S. Malyshev

  2. Nizhni Novgorod State University, ul. Gagarina 23, 603950, Nizhni Novgorod, Russia

    D. S. Malyshev

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  1. D. S. Malyshev
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Correspondence to D. S. Malyshev.

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Original Russian Text © D.S. Malyshev, 2013, published in Diskretnyi Analiz i Issledovanie Operatsii, 2013, Vol. 20, No. 2, pp. 75–87.

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Malyshev, D.S. Expanding operators for the independent set problem. J. Appl. Ind. Math. 7, 412–419 (2013). https://doi.org/10.1134/S1990478913030149

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  • DOI: https://doi.org/10.1134/S1990478913030149

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