{"paper":{"title":"An ${\\cal O}(n\\sqrt{m})$ algorithm for the weighted stable set problem in {claw, net}-free graphs with $\\alpha(G) \\ge 4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Antonio Sassano, Paolo Nobili","submitted_at":"2015-01-23T16:04:19Z","abstract_excerpt":"In this paper we show that a connected {claw, net}-free graph $G(V, E)$ with $\\alpha(G) \\ge 4$ is the union of a strongly bisimplicial clique $Q$ and at most two clique-strips. A clique is strongly bisimplicial if its neighborhood is partitioned into two cliques which are mutually non-adjacent and a clique-strip is a sequence of cliques $\\{H_0, \\dots, H_p\\}$ with the property that $H_i$ is adjacent only to $H_{i-1}$ and $H_{i+1}$. By exploiting such a structure we show how to solve the Maximum Weight Stable Set Problem in such a graph in time ${\\cal O}(|V|\\sqrt{|E|})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05851","kind":"arxiv","version":2},"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"}