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Diskretn. Anal. Issled. Oper., 2017, Volume 24, Number 1, Pages 56–80 (Mi da863)  

$1$-Triangle graphs and perfect neighborhood sets

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

Belarusian State University, 4 Nezavisimosti Ave., 220030 Minsk, Belarus

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 established within the class of $1$-triangle graphs for a range of graph-theoretical parameters related to independence and domination. In particular, $\mathrm{NP}$-completeness is established for the minimum perfect neighborhood set problem in the class of all graphs. Bibliogr. 20.

Keywords: triangle graph, edge-simplicial graph, characterization, perfect neighborhood set, $\mathrm{NP}$-completeness.

Funding Agency Grant Number
Belarusian Republican Foundation for Fundamental Research Ф15МЛД-022


DOI: https://doi.org/10.17377/daio.2017.24.532

Full text: PDF file (393 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:1, 58–69

Bibliographic databases:

UDC: 519.17
Received: 16.03.2016
Revised: 27.06.2016

Citation: P. A. Irzhavskii, Yu. A. Kartynnik, Yu. L. Orlovich, “$1$-Triangle graphs and perfect neighborhood sets”, Diskretn. Anal. Issled. Oper., 24:1 (2017), 56–80; J. Appl. Industr. Math., 11:1 (2017), 58–69

Citation in format AMSBIB
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\by P.~A.~Irzhavskii, Yu.~A.~Kartynnik, Yu.~L.~Orlovich
\paper $1$-Triangle graphs and perfect neighborhood sets
\jour Diskretn. Anal. Issled. Oper.
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\vol 24
\issue 1
\pages 56--80
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\crossref{https://doi.org/10.17377/daio.2017.24.532}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3622065}
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\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
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\pages 58--69
\crossref{https://doi.org/10.1134/S1990478917010070}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85013919134}


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