{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:E3BY2IEQ3OAHFS37TYVPVF232H","short_pith_number":"pith:E3BY2IEQ","schema_version":"1.0","canonical_sha256":"26c38d2090db8072cb7f9e2afa975bd1e2d9e13422748dbda3db1dc769f1716d","source":{"kind":"arxiv","id":"1411.2928","version":2},"attestation_state":"computed","paper":{"title":"Homothetic Polygons and Beyond: Intersection Graphs, Recognition, and Maximum Clique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jan Kratochv\\'il, Joshua Terhaar, Konstanty Junosza-Szaniawski, Martin Pergel, Matthew Szczepankiewicz, Pawe{\\l} Rz\\k{a}\\.zewski, Sean Kafer, Valentin E. Brimkov","submitted_at":"2014-11-11T19:14:19Z","abstract_excerpt":"We study the {\\sc Clique} problem in classes of intersection graphs of convex sets in the plane. The problem is known to be NP-complete in convex-set intersection graphs and straight-line-segment intersection graphs, but solvable in polynomial time in intersection graphs of homothetic triangles. We extend the latter result by showing that for every convex polygon $P$ with sides parallel to $k$ directions, every $n$-vertex graph which is an intersection graph of homothetic copies of $P$ contains at most $n^{k}$ inclusion-wise maximal cliques. We actually prove this result for a more general cla"},"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":"1411.2928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-11-11T19:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"0a5a69460f366df7c5f5383ebb202b140691a43e2377d2fc0609ae482fdc6ca6","abstract_canon_sha256":"cfca0f5b1029198cb6ba3f8ea046d8f4cc494ce27c5557030108ead1685b745a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:27.933871Z","signature_b64":"NCt8+ZztP5QvvH/WT2teuwtRQm3wI0QtpC3qwus0I90/qz/kSsq9oC97IPHQDcGxm1Va4jJ462O66wC+VC+hDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26c38d2090db8072cb7f9e2afa975bd1e2d9e13422748dbda3db1dc769f1716d","last_reissued_at":"2026-05-18T00:59:27.933202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:27.933202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homothetic Polygons and Beyond: Intersection Graphs, Recognition, and Maximum Clique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jan Kratochv\\'il, Joshua Terhaar, Konstanty Junosza-Szaniawski, Martin Pergel, Matthew Szczepankiewicz, Pawe{\\l} Rz\\k{a}\\.zewski, Sean Kafer, Valentin E. Brimkov","submitted_at":"2014-11-11T19:14:19Z","abstract_excerpt":"We study the {\\sc Clique} problem in classes of intersection graphs of convex sets in the plane. The problem is known to be NP-complete in convex-set intersection graphs and straight-line-segment intersection graphs, but solvable in polynomial time in intersection graphs of homothetic triangles. We extend the latter result by showing that for every convex polygon $P$ with sides parallel to $k$ directions, every $n$-vertex graph which is an intersection graph of homothetic copies of $P$ contains at most $n^{k}$ inclusion-wise maximal cliques. We actually prove this result for a more general cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2928","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.2928","created_at":"2026-05-18T00:59:27.933313+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.2928v2","created_at":"2026-05-18T00:59:27.933313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2928","created_at":"2026-05-18T00:59:27.933313+00:00"},{"alias_kind":"pith_short_12","alias_value":"E3BY2IEQ3OAH","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"E3BY2IEQ3OAHFS37","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"E3BY2IEQ","created_at":"2026-05-18T12:28:25.294606+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H","json":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H.json","graph_json":"https://pith.science/api/pith-number/E3BY2IEQ3OAHFS37TYVPVF232H/graph.json","events_json":"https://pith.science/api/pith-number/E3BY2IEQ3OAHFS37TYVPVF232H/events.json","paper":"https://pith.science/paper/E3BY2IEQ"},"agent_actions":{"view_html":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H","download_json":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H.json","view_paper":"https://pith.science/paper/E3BY2IEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.2928&json=true","fetch_graph":"https://pith.science/api/pith-number/E3BY2IEQ3OAHFS37TYVPVF232H/graph.json","fetch_events":"https://pith.science/api/pith-number/E3BY2IEQ3OAHFS37TYVPVF232H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H/action/storage_attestation","attest_author":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H/action/author_attestation","sign_citation":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H/action/citation_signature","submit_replication":"https://pith.science/pith/E3BY2IEQ3OAHFS37TYVPVF232H/action/replication_record"}},"created_at":"2026-05-18T00:59:27.933313+00:00","updated_at":"2026-05-18T00:59:27.933313+00:00"}