Abstract
A graph G is P5-reducible if every vertex of G lies in at most one induced P5 (path on five vertices). We show that a number of interesting results concerning P5-free graphs can be extended to P5-reducible graphs, namely: the existence of a dominating clique or P3, the fact that k-colorability can be decided in polynomial time (for fixed k), and the fact that a maximum stable set can be found in polynomial time in the class of k-colorable P5-reducible graphs (for fixed k).
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