{"paper":{"title":"Offensive alliances in cubic graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. A. Rodriguez, J. M. Sigarreta","submitted_at":"2006-09-30T15:23:39Z","abstract_excerpt":"An offensive alliance in a graph $\\Gamma=(V,E)$ is a set of vertices $S\\subset V$ where for every vertex $v$ in its boundary it holds that the majority of vertices in $v$'s closed neighborhood are in $S$. In the case of strong offensive alliance, strict majority is required. An alliance $S$ is called global if it affects every vertex in $V\\backslash S$, that is, $S$ is a dominating set of $\\Gamma$. The global offensive alliance number $\\gamma_o(\\Gamma)$ (respectively, global strong offensive alliance number $\\gamma_{\\hat{o}}(\\Gamma)$) is the minimum cardinality of a global offensive (respectiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610023","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"}