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

Authors:
Vladimir E. Alekseev
Affiliations:
University of Nizhny Novgorod, Gagarina 23, Nizhny Novgorod 603600, Russia
Venue:
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Year:
2003

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Abstract

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.