{"paper":{"title":"A Sublinear Bound on the Cop Throttling Number of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anthony Bonato, Sean English","submitted_at":"2019-01-25T18:24:55Z","abstract_excerpt":"We provide a sublinear bound on the cop throttling number of a connected graph. Related to the graph searching game Cops and Robbers, the cop throttling number, written $\\mathrm{th}_c(G)$, is given by $\\mathrm{th}_c(G)=\\min_k\\{k+\\mathrm{capt}_k(G)\\}$, in which $\\mathrm{capt}_k(G)$ is the $k$-capture time, or the length of a game of Cops and Robbers with $k$ cops on the graph $G$, assuming both players play optimally.\n  No general sublinear bound was known on the cop throttling number of a connected graph. Towards a question asked by Breen et al., we prove that $\\mathrm{th}_c(G)\\leq \\frac{(2+o("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09011","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"}