{"paper":{"title":"Majority out-dominating functions in digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akbar Azami, Karam Ebadi, Mart\\'in Manrique","submitted_at":"2013-11-03T15:19:41Z","abstract_excerpt":"At least two different notions have been published under the name \"majority domination in graphs\": Majority dominating functions and majority dominating sets. In this work we extend the former concept to digraphs. Given a digraph $D=(V,A),$ a function $f : V \\rightarrow \\{-1,1\\}$ such that $f(N^+[v])\\geq1$ for at least half of the vertices $v$ in $V$ is a majority out-dominating function (MODF) of $D.$ The weight of a MODF $f$ is $w(f)=\\sum\\limits_{v\\in V}f(v),$ and the minimum weight of a MODF in $D$ is the majority out-domination number of $D,$ denoted $\\gamma^+_{maj}(D).$ In this work we in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0475","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"}