{"paper":{"title":"The clique problem on inductive $k$-independent graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"George Manoussakis","submitted_at":"2014-10-13T13:38:47Z","abstract_excerpt":"A graph is inductive $k$-independent if there exists and ordering of its vertices $v_{1},...,v_{n}$ such that $\\alpha(G[N(v_{i})\\cap V_{i}])\\leq k $ where $N(v_{i})$ is the neighborhood of $v_{i}$, $V_{i}=\\{v_{i},...,v_{n}\\}$ and $\\alpha$ is the independence number. In this article, by answering to a question of [Y.Ye, A.Borodin, Elimination graphs, ACM Trans. Algorithms 8 (2) (2012) 14:1-14:23], we design a polynomial time approximation algorithm with ratio {$\\overline{\\Delta} \\slash log(log(\\overline{ \\Delta}) \\slash k)$ for the maximum clique and also show that the decision version of this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3302","kind":"arxiv","version":6},"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"}