{"paper":{"title":"An ${\\cal O}(m\\log n)$ algorithm for the weighted stable set problem in claw-free graphs with $\\alpha({G}) \\le 3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Antonio Sassano, Paolo Nobili","submitted_at":"2015-01-23T11:33:07Z","abstract_excerpt":"In this paper we show how to solve the \\emph{Maximum Weight Stable Set Problem} in a claw-free graph $G(V, E)$ with $\\alpha(G) \\le 3$ in time ${\\cal O}(|E|\\log|V|)$. More precisely, in time ${\\cal O}(|E|)$ 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 ${\\cal O}(|E|\\log|V|)$ a maximum stable set of $G$. This improves the bound of ${\\cal O}(|E||V|)$ due to Faenza et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}