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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 $\\delta(G)\\ge 2$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0705.3748","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cs.DM","submitted_at":"2007-05-25T11:19:03Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"b992ac3f871ddc1141ac6446b9238980707f24100dff4a59fd3ff4d69b3c9460","abstract_canon_sha256":"4d6396d2135f8f336a7b7676245668ca8ff2556a50c36e74b503004688e88397"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:16.478075Z","signature_b64":"OohPxlWeRN1GBov30n1qIY9bieGmkftyClaAZZ0QfIR7j6h51in+ZaK/qJGFvXSnVXcuR57y7e33TthTptUGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94df4224d320eedc116b698690c6785f384e535a28f9ce61d0a1c342f82886de","last_reissued_at":"2026-05-18T04:09:16.477677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:16.477677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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