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 Diskretn. Anal. Issled. Oper., 2013, Volume 20, Issue 2, Pages 75–87 (Mi da727)

Extending operators for the independent set problem

D. S. Malyshevab

a Nizhniy Novgorod Higher School of Economics, Nizhniy Novgorod, Russia
b Nizhniy Novgorod State University, Nizhniy Novgorod, Russia

Abstract: The notion of an extending operator for the independent set problem is introduced. This notion is a useful tool for constructive obtaining of new cases with the effective 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 the same in the class $Free(\{P_5,C_5,G\circ\overline K_2,G\oplus K_{1,p}\})$ for any $p$. New hereditary subsets of $Free(\{P_5,C_5\})$ with the independent set problem solvable in polynomial time that are not results of application of the specified operators are found. Bibliogr. 22.

Keywords: independent set problem, theory of computational complexity, extending operator, effective algorithm.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:3, 412–419

Bibliographic databases:

UDC: 519.178
Revised: 20.04.2012

Citation: D. S. Malyshev, “Extending operators for the independent set problem”, Diskretn. Anal. Issled. Oper., 20:2 (2013), 75–87; J. Appl. Industr. Math., 7:3 (2013), 412–419

Citation in format AMSBIB
\Bibitem{Mal13} \by D.~S.~Malyshev \paper Extending operators for the independent set problem \jour Diskretn. Anal. Issled. Oper. \yr 2013 \vol 20 \issue 2 \pages 75--87 \mathnet{http://mi.mathnet.ru/da727} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3113402} \transl \jour J. Appl. Industr. Math. \yr 2013 \vol 7 \issue 3 \pages 412--419 \crossref{https://doi.org/10.1134/S1990478913030149}