Abstract
The complexity status of the stable set problem in the class of P 5-free graphs is unknown. In the present paper we study an approach to the problem based on finding augmenting graphs. The main result is that the stable set problem in the class of P 5-free graphs is polynomially equivalent to the problem of finding augmenting graphs containing a P 4. We apply this result to detect a new infinite family of graph classes where the problem has a polynomial time solution. The new family generalizes several previously known results.
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