{"paper":{"title":"Certified domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jerzy Topp, Magda Dettlaff, Magdalena Lema\\'nska, Pawe{\\l} \\.Zyli\\'nski, Rados{\\l}aw Ziemann","submitted_at":"2016-06-10T10:21:38Z","abstract_excerpt":"Imagine that we are given a set $D$ of officials and a set $W$ of civils. For each civil $x \\in W$, there must be an official $v \\in D$ that can serve $x$, and whenever any such $v$ is serving $x$, there must also be another civil $w \\in W$ that observes $v$, that is, $w$ may act as a kind of witness, to avoid any abuse from $v$. What is the minimum number of officials to guarantee such a service, assuming a given social network?\n  In this paper, we introduce the concept of certified domination that perfectly models the aforementioned problem. Specifically, a dominating set $D$ of a graph $G=("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03257","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"}