Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Stable sets in certain P6-free graphs
Discrete Applied Mathematics
Finding augmenting chains in extensions of claw-free graphs
Information Processing Letters
An augmenting graph approach to the stable set problem in P5-free graphs
Discrete Applied Mathematics
Stable sets in two subclasses of banner-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Polynomial algorithm for finding the largest independent sets in graphs without forks
Discrete Applied Mathematics
Augmenting graphs for independent sets
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Augmenting chains in graphs without a skew star
Journal of Combinatorial Theory Series B
Parameterized algorithms for the independent set problem in some hereditary graph classes
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
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Method of augmenting graphs is a general approach to solve the maximum independent set problem. As the problem is generally NP-hard, no polynomial time algorithms are available to implement the method. However, when restricted to particular classes of graphs, the approach may lead to efficient solutions. A famous example of this type is the maximum matching algorithm: it finds a maximum matching in a graph G, which is equivalent to finding a maximum independent set in the line graph of G. In the particular case of line graphs, the method reduces to finding augmenting (alternating) chains. Recent investigations of more general classes of graphs revealed many more types of augmenting graphs. In the present paper we study the problem of finding augmenting graphs different from chains. To simplify this problem, we introduce the notion of a redundant set. This allows us to reduce the problem to finding some basic augmenting graphs. As a result, we obtain a polynomial time solution to the maximum independent set problem in a class of graphs which extends several previously studied classes including the line graphs.