{"paper":{"title":"Rainbow domination and related problems on some classes of perfect graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Hsian-Hsuan Liu, Hung-Lung Wang, Ton Kloks, Wing-Kai Hon","submitted_at":"2015-02-26T10:28:43Z","abstract_excerpt":"Let $k \\in \\mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \\rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\\emptyset$, $f(N(x)) =[k]$. The rainbow domination number $\\gamma_{kr}(G)$ is the minimum of $\\sum_{x \\in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07492","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"}