{"paper":{"title":"Neighborhood covering and independence on two superclasses of cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Guillermo Dur\\'an, Mart\\'in D. Safe, Xavier S. Warnes","submitted_at":"2016-01-01T00:02:19Z","abstract_excerpt":"Given a simple graph $G$, a set $C \\subseteq V(G)$ is a neighborhood cover set if every edge and vertex of $G$ belongs to some $G[v]$ with $v \\in C$, where $G[v]$ denotes the subgraph of $G$ induced by the closed neighborhood of the vertex $v$. Two elements of $E(G) \\cup V(G)$ are neighborhood-independent if there is no vertex $v\\in V(G)$ such that both elements are in $G[v]$. A set $S\\subseteq V(G)\\cup E(G)$ is neighborhood-independent if every pair of elements of $S$ is neighborhood-independent. Let $\\rho_{\\mathrm n}(G)$ be the size of a minimum neighborhood cover set and $\\alpha_{\\mathrm n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00032","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"}