{"paper":{"title":"Lower bounds on the dilation of plane spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Adrian Dumitrescu, Anirban Ghosh","submitted_at":"2015-09-23T23:42:00Z","abstract_excerpt":"(I) We exhibit a set of 23 points in the plane that has dilation at least $1.4308$, improving the previously best lower bound of $1.4161$ for the worst-case dilation of plane spanners.\n  (II) For every integer $n\\geq13$, there exists an $n$-element point set $S$ such that the degree 3 dilation of $S$ denoted by $\\delta_0(S,3) \\text{ equals } 1+\\sqrt{3}=2.7321\\ldots$ in the domain of plane geometric spanners. In the same domain, we show that for every integer $n\\geq6$, there exists a an $n$-element point set $S$ such that the degree 4 dilation of $S$ denoted by $\\delta_0(S,4) \\text{ equals } 1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07181","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"}