{"paper":{"title":"Shorter Labeling Schemes for Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cyril Gavoille (LaBRI), Marthe Bonamy (LaBRI), Michal Pilipczuk","submitted_at":"2019-08-09T07:08:23Z","abstract_excerpt":"An \\emph{adjacency labeling scheme} for a given class of graphs is  an algorithm that for every graph $G$ from the class, assigns bit  strings (labels) to vertices of $G$ so that for any two vertices  $u,v$, whether $u$ and $v$ are adjacent can be determined by a fixed  procedure that examines only their labels. It is known that planar  graphs with $n$ vertices admit a labeling scheme with labels of bit length  $(2+o(1))\\log{n}$.  In this work we improve this bound by designing a labeling scheme  with labels of bit length $(\\frac{4}{3}+o(1))\\log{n}$.      In graph-theoretical terms, this impli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03341","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/1908.03341/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"}