A Polynomial-Time Algorithm for the Independent Set Problem in {P10, C4, C6}-Free Graphs

Abstract

We consider the independent set problem, a classical NP-hard optimization problem that remains hard even under substantial restrictions on the input graphs. The complexity status of the problem is unknown for the classes of $$P:k$$ -free graphs for all $$k\ge 7$$ and for the class of even-hole-free graphs, that is, graphs not containing any even induced cycles. Using the technique of augmenting graphs we show that the independent set problem is solvable in polynomial time in the class of even-hole-free graphs not containing an induced path on 10 vertices. Our result is developed in the context of the more general class of $$\{P:{10},C_4,C_6\}$$ -free graphs.