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.
E. Husić did most of his work on the paper while he was a student at the University of Primorska and École normale supérieure de Lyon. Several ideas for the proofs were developed in his master thesis [14].
M. Milanič—The work is supported in part by the Slovenian Research Agency (I0-0035, research program P1-0285 and research projects J1-9110, N1-0102).
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The authors are grateful to the anonymous reviewers for many helpful remarks.
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Husić, E., Milanič, M. (2019). A Polynomial-Time Algorithm for the Independent Set Problem in \(\{{P_{10}},C_4,C_6\}\)-Free Graphs. In: Sau, I., Thilikos, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2019. Lecture Notes in Computer Science(), vol 11789. Springer, Cham. https://doi.org/10.1007/978-3-030-30786-8_21
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