EN|RU Volume 19, No 3, 2012, P. 58-64 UDC 519.178 D. S. Malyshev Effective solvability of the independent set problem in a class of graphs without induced path and cycle with five vertices and a big clique Abstract: An algorithm for finding the independence number of a $n$-vertex graph from the class $\operatorname{Free}(\{P_5,C_5,K_p\})$ in time $O(n^{p+O(1)})$ is proposed. Bibliogr. 10. Keywords: the independent set problem, computational complexity, polynomial algorithm. Malyshev Dmitrii Sergeevich 1,2 1. Nizhniy Novgorod Higher School of Economics, 25/12 B. Pecherskaya str., 603155 Nizhny Novgorod, Russia 2. Nizhniy Novgorod State University, 23 Gagarina ave., 603950 Nizhniy Novgorod, Russia e-mail: dsmalyshev@rambler.ru © Sobolev Institute of Mathematics, 2015