English version:
Journal of Applied and Industrial Mathematics, 2017, 11:1, 58-69

Volume 24, No 1, 2017, P. 56-80

UDC 519.17
P. A. Irzhavskii, Yu. A. Kartynnik, and Yu. L. Orlovich
1-Triangle graphs and perfect neighborhood sets

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, 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, NP-completeness.

DOI: 10.17377/daio.2017.24.532

Pavel A. Irzhavskii 1
Yury A. Kartynnik 1

Yury L. Orlovich 1
1. Belarusian State University,
4 Nezavisimosti Ave., 220030 Minsk, Belarus
e-mail: irzhavski@bsu.by, kartynnik@bsu.by, orlovich@bsu.by

Received 16 March 2016
Revised 27 June 2016


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