An ${\cal O}(m\log n)$ algorithm for the weighted stable set problem in claw-free graphs with $\alpha({G}) \le 3$

In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G(V,E) with α(G) ≤ 3 in time O(|E| log |V |). More precisely, in time O(|E|) we check whether α(G) ≤ 3 or produce a stable set with cardinality at least 4; moreover, if α(G) ≤ 3 we produce in time O(|E| log |V |) a maximum stable set of G. This improves the bound of O(|E||V |) due to Faenza et alii ([2]).

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