{"paper":{"title":"Linear kernels for k-tuple and liar's domination in bounded genus graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Arijit Bishnu, Arijit Ghosh, Subhabrata Paul","submitted_at":"2013-09-21T11:07:24Z","abstract_excerpt":"A set $D\\subseteq V$ is called a $k$-tuple dominating set of a graph $G=(V,E)$ if $\\left| N_G[v] \\cap D \\right| \\geq k$ for all $v \\in V$, where $N_G[v]$ denotes the closed neighborhood of $v$. A set $D \\subseteq V$ is called a liar's dominating set of a graph $G=(V,E)$ if (i) $\\left| N_G[v] \\cap D \\right| \\geq 2$ for all $v\\in V$ and (ii) for every pair of distinct vertices $u, v\\in V$, $\\left| (N_G[u] \\cup N_G[v]) \\cap D \\right| \\geq 3$. Given a graph $G$, the decision versions of $k$-Tuple Domination Problem and the Liar's Domination Problem are to check whether there exists a $k$-tuple dom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5461","kind":"arxiv","version":4},"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"}