{"paper":{"title":"The k-Tuple Domatic Number of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adel P. Kazemi","submitted_at":"2011-06-28T08:24:04Z","abstract_excerpt":"For every positive integer $k$, a set $S$ of vertices in a graph $G=(V,E)$ is a $k$-tuple dominating set of $G$ if every vertex of $V-S$ is adjacent to least $k$ vertices and every vertex of $S$ is adjacent to least $k-1$ vertices in $S$. The minimum cardinality of a $k$-tuple dominating set of $G$ is the $k$-tuple domination number of $G$. When $k=1$, a $k$-tuple domination number is the well-studied domination number. We define the $k$-tuple domatic number of $G$ as the largest number of sets in a partition of $V$ into $k$-tuple dominating sets. Recall that when $k=1$, a $k$-tuple domatic nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5589","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"}