{"paper":{"title":"On the complexity of the outer-connected bondage and the outer-connected reinforcement problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DM","authors_text":"A. Shakiba, M. Hashemipour, M. R. Hooshmandasl","submitted_at":"2018-02-02T12:04:12Z","abstract_excerpt":"Let $G=(V,E)$ be a graph. A subset $S \\subseteq V$ is a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A set $\\tilde{D} \\subseteq V$ of a graph $G=(V,E) $ is called an outer-connected dominating set for $G$ if (1) $\\tilde{D}$ is a dominating set for $G$, and (2) $G [V \\setminus \\tilde{D}]$, the induced subgraph of $G$ by $V \\setminus \\tilde{D}$, is connected. The minimum size among all outer-connected dominating sets of $G$ is called the outer-connected domination number of $G$ and is denoted by $\\tilde{\\gamma}_c(G)$. We define the outer-connected bondage numb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00649","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"}