An O(mlogn) algorithm for the weighted stable set problem in claw-free graphs with α(G)≤3 - Nobili, Paolo; Sassano, Antonio (Mathematical programming, 2017)
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 weight stable set of G . This improves the bound of O ( | E | | V | ) due to Faenza, Oriolo and Stauffer.