{"paper":{"title":"Lattice spanners of low degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.MG","authors_text":"Adrian Dumitrescu, Anirban Ghosh","submitted_at":"2016-02-13T21:19:12Z","abstract_excerpt":"Let $\\delta_0(P,k)$ denote the degree $k$ dilation of a point set $P$ in the domain of plane geometric spanners. If $\\Lambda$ is the infinite square lattice, it is shown that $1+\\sqrt{2} \\leq \\delta_0(\\Lambda,3) \\leq (3+2\\sqrt2) \\, 5^{-1/2} = 2.6065\\ldots$ and $\\delta_0(\\Lambda,4) = \\sqrt{2}$. If $\\Lambda$ is the infinite hexagonal lattice, it is shown that $\\delta_0(\\Lambda,3) = 1+\\sqrt{3}$ and $\\delta_0(\\Lambda,4) = 2$. All our constructions are planar lattice tilings constrained to degree $3$ or $4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04381","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":""},"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"}