EN|RU Volume 20, No 2, 2013, P. 75-87 UDC 519.178 Malyshev D. S. Extending operators for the independent set problem 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. Malyshev Dmitriy Sergeevich 1,2 1. Nizhniy Novgorod Higher School of Economics, 25/12 B. Pecherskaya St., 603155 Nizhniy Novgorod, Russia 2. Nizhniy Novgorod State University, 23 Gagarin Ave., 603950 Nizhniy Novgorod, Russia e-mail: dsmalyshev@rambler.ru © Sobolev Institute of Mathematics, 2015