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1-Triangle graphs and perfect neighborhood sets

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Abstract

A graph is called a 1-triangle if, for its every maximal independent set I, every edge of this graph with both endvertices not belonging to I is contained exactly in one triangle with a vertex of I. We obtain a characterization of 1-triangle graphs which implies a polynomial time recognition algorithm. Computational complexity is establishedwithin the class of 1-triangle graphs for a range of graph-theoretical parameters related to independence and domination. In particular, NP-completeness is established for the minimum perfect neighborhood set problem in the class of all graphs.

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Authors and Affiliations

  1. Belarusian State University, pr. Nezavisimosti 4, Minsk, 220030, Belarus

    P. A. Irzhavskii, Yu. A. Kartynnik & Yu. L. Orlovich

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  1. P. A. Irzhavskii
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  2. Yu. A. Kartynnik
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  3. Yu. L. Orlovich
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Correspondence to P. A. Irzhavskii.

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Original Russian Text © P.A. Irzhavskii, Yu.A. Kartynnik, Yu.L. Orlovich, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 1, pp. 56–80.

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Irzhavskii, P.A., Kartynnik, Y.A. & Orlovich, Y.L. 1-Triangle graphs and perfect neighborhood sets. J. Appl. Ind. Math. 11, 58–69 (2017). https://doi.org/10.1134/S1990478917010070

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  • DOI: https://doi.org/10.1134/S1990478917010070

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