Abstract
In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G(V, E) with \(\alpha (G) \le 3\) in time \(\mathcal{O}(|E|\log |V|)\). More precisely, in time \(\mathcal{O}(|E|)\) we check whether \(\alpha (G) \le 3\) or produce a stable set with cardinality at least 4; moreover, if \(\alpha (G) \le 3\) we produce in time \(\mathcal{O}(|E|\log |V|)\) a maximum weight stable set of G. This improves the bound of \(\mathcal{O}(|E||V|)\) due to Faenza, Oriolo and Stauffer.
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Nobili, P. Sassano, A.: An \({O}(n^2 \log n)\) algorithm for the weighted stable set problem in claw-free graphs, CoRR abs/1501.05775. http://arxiv.org/abs/1501.05775
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We thank the anonymous referee whose suggestions have allowed us to improve the quality of the presentation.
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Nobili, P., Sassano, A. An \(\mathcal{O}(m\log n)\) algorithm for the weighted stable set problem in claw-free graphs with \(\alpha ({G}) \le 3\) . Math. Program. 164, 157–165 (2017). https://doi.org/10.1007/s10107-016-1080-9
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DOI: https://doi.org/10.1007/s10107-016-1080-9