{"paper":{"title":"Changing and unchanging 2-rainbow independent domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"M. Soroudi, Pu Wu, Shaohui Wang, S.M. Sheikholeslami, Vladimir Samodivkin, Zehui Shao","submitted_at":"2018-09-29T18:03:30Z","abstract_excerpt":"For a function $f : V(G ) \\rightarrow \\{0, 1, 2\\}$ we denote by $V_i$ the set of vertices to which the value $i$ is assigned by $f$, i.e. $V_i = \\{ x \\in V (G ) : f(x ) = i \\}$. If a function $f: V(G) \\rightarrow \\{0,1,2\\}$ satisfying the condition that $V_i$ is independent for $i \\in \\{1,2\\}$ and every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = i$ for each $i \\in \\{1,2\\}$, then $f$ is called a 2-rainbow independent dominating function (2RiDF). The weight $w(f)$ of a 2RiDF $f$ is the value $w(f) = |V_1|+|V_2|$. The minimum weight of a 2RiDF on a gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00246","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"}