{"paper":{"title":"Improved Bounds for Guarding Plane Graphs with Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ahmad Biniaz, Aur\\'elien Ooms, Prosenjit Bose, Sander Verdonschot","submitted_at":"2018-04-19T13:26:19Z","abstract_excerpt":"An \"edge guard set\" of a plane graph $G$ is a subset $\\Gamma$ of edges of $G$ such that each face of $G$ is incident to an endpoint of an edge in $\\Gamma$. Such a set is said to guard $G$. We improve the known upper bounds on the number of edges required to guard any $n$-vertex embedded planar graph $G$:\n  1- We present a simple inductive proof for a theorem of Everett and Rivera-Campo (1997) that $G$ can be guarded with at most $ \\frac{2n}{5}$ edges, then extend this approach with a deeper analysis to yield an improved bound of $\\frac{3n}{8}$ edges for any plane graph.\n  2- We prove that ther"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07150","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"}