On easy and hard hereditary classes of graphs with respect to the independent set problem

In this paper we introduce the concept of a boundary class, which is a helpful tool for classification of hereditary classes of graphs according to the complexity of the independent set problem. It is shown that in a class X defined by a finite set of forbidden induced subgraphs, the problem is NP-hard if and only if X includes a boundary class. The paper presents a particular boundary class and establishes several new polynomially solvable cases for the independent set problem. (C) 2003 Published by Elsevier B.V.