{"paper":{"title":"Cop numbers of periodic graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Simard, Jean-Lou De Carufel, Nicola Santoro, Paola Flocchini","submitted_at":"2023-10-20T16:05:58Z","abstract_excerpt":"A \\emph{periodic graph} ${\\cal G}=(G_0, G_1, G_2, \\dots)$ with period $p$ is an infinite periodic sequence of graphs $G_i = G_{i + p} = (V,E_i)$, where $i \\geq 0$. The graph $G=(V,\\cup_i E_i)$ is called the footprint of ${\\cal G}$. Recently, the arena where the Cops and Robber game is played has been extended from a graph to a periodic graph; in this case, the \\emph{cop number} is also the minimum number of cops sufficient for capturing the robber. We study the connections and distinctions between the cop number $c({\\cal G})$ of a periodic graph ${\\cal G}$ and the cop number $c(G)$ of its foot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.13616","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.13616/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}