{"paper":{"title":"On the Obfuscation Complexity of Planar Graphs","license":"","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DM","authors_text":"Oleg Verbitsky","submitted_at":"2007-05-25T11:19:03Z","abstract_excerpt":"Being motivated by John Tantalo's Planarity Game, we consider straight line plane drawings of a planar graph $G$ with edge crossings and wonder how obfuscated such drawings can be. We define $obf(G)$, the obfuscation complexity of $G$, to be the maximum number of edge crossings in a drawing of $G$. Relating $obf(G)$ to the distribution of vertex degrees in $G$, we show an efficient way of constructing a drawing of $G$ with at least $obf(G)/3$ edge crossings. We prove bounds $(\\delta(G)^2/24-o(1))n^2 < \\obf G <3 n^2$ for an $n$-vertex planar graph $G$ with minimum vertex degree $\\delta(G)\\ge 2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3748","kind":"arxiv","version":3},"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"}