{"paper":{"title":"Perfect and quasiperfect domination in trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carmen Hernando, Ignacio M. Pelayo, Jos\\'e C\\'aceres, Mar\\'ia Luz Puertas, Merc\\'e Mora","submitted_at":"2015-05-29T09:30:39Z","abstract_excerpt":"A $k-$quasiperfect dominating set ($k\\ge 1$) of a graph $G$ is a vertex subset $S$ such that every vertex not in $S$ is adjacent to at least one and at most k vertices in $S$. The cardinality of a minimum k-quasiperfect dominating set in $G$ is denoted by $\\gamma_{\\stackrel{}{1k}}(G)$. Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept. The quasiperfect domination chain $\\gamma_{\\stackrel{}{11}}(G)\\ge\\gamma_{\\stackrel{}{12}}(G)\\ge\\dots\\ge\\gamma_{\\stackrel{}{1\\Delta}}(G)=\\gamma(G)$, indicates what it is lost in size when you move tow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07967","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"}