{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:I3EZJJ44IOC7IKPISG5UBW6P4L","short_pith_number":"pith:I3EZJJ44","schema_version":"1.0","canonical_sha256":"46c994a79c4385f429e891bb40dbcfe2d4c923c25ee1a5e3df8a0e7f4dd61d9f","source":{"kind":"arxiv","id":"1303.6567","version":1},"attestation_state":"computed","paper":{"title":"Excluding Graphs as Immersions in Surface Embedded Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Archontia C. Giannopoulou, Dimitrios M. Thilikos, Marcin Kaminski","submitted_at":"2013-03-26T17:45:11Z","abstract_excerpt":"We prove a structural characterization of graphs that forbid a fixed graph $H$ as an immersion and can be embedded in a surface of Euler genus $\\gamma$. In particular, we prove that a graph $G$ that excludes some connected graph $H$ as an immersion and is embedded in a surface of Euler genus $\\gamma$ has either \"small\" treewidth (bounded by a function of $H$ and $\\gamma$) or \"small\" edge connectivity (bounded by the maximum degree of $H$). Using the same techniques we also prove an excluded grid theorem on bounded genus graphs for the immersion relation."},"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":"1303.6567","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-03-26T17:45:11Z","cross_cats_sorted":[],"title_canon_sha256":"36a74ac85ef8515e542efe409f6d8e97546aa7dadd2b75bb966a85232a5bf7c5","abstract_canon_sha256":"a9c39eae0839f8cfc53e1ee1b4f1f4edf1c62524aceed2961385176ba4dcd821"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:49.039297Z","signature_b64":"K3pySmBBo+t5kt93cYMcU1Jm6Tz8+dXVinoicZwEvCxpv6XlDIanuAoU/510VPQ92F35jc/EA2R5CiDAWJMuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46c994a79c4385f429e891bb40dbcfe2d4c923c25ee1a5e3df8a0e7f4dd61d9f","last_reissued_at":"2026-05-18T03:29:49.038621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:49.038621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Excluding Graphs as Immersions in Surface Embedded Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Archontia C. Giannopoulou, Dimitrios M. Thilikos, Marcin Kaminski","submitted_at":"2013-03-26T17:45:11Z","abstract_excerpt":"We prove a structural characterization of graphs that forbid a fixed graph $H$ as an immersion and can be embedded in a surface of Euler genus $\\gamma$. In particular, we prove that a graph $G$ that excludes some connected graph $H$ as an immersion and is embedded in a surface of Euler genus $\\gamma$ has either \"small\" treewidth (bounded by a function of $H$ and $\\gamma$) or \"small\" edge connectivity (bounded by the maximum degree of $H$). Using the same techniques we also prove an excluded grid theorem on bounded genus graphs for the immersion relation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6567","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.6567","created_at":"2026-05-18T03:29:49.038751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6567v1","created_at":"2026-05-18T03:29:49.038751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6567","created_at":"2026-05-18T03:29:49.038751+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3EZJJ44IOC7","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3EZJJ44IOC7IKPI","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3EZJJ44","created_at":"2026-05-18T12:27:46.883200+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/I3EZJJ44IOC7IKPISG5UBW6P4L","json":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L.json","graph_json":"https://pith.science/api/pith-number/I3EZJJ44IOC7IKPISG5UBW6P4L/graph.json","events_json":"https://pith.science/api/pith-number/I3EZJJ44IOC7IKPISG5UBW6P4L/events.json","paper":"https://pith.science/paper/I3EZJJ44"},"agent_actions":{"view_html":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L","download_json":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L.json","view_paper":"https://pith.science/paper/I3EZJJ44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6567&json=true","fetch_graph":"https://pith.science/api/pith-number/I3EZJJ44IOC7IKPISG5UBW6P4L/graph.json","fetch_events":"https://pith.science/api/pith-number/I3EZJJ44IOC7IKPISG5UBW6P4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L/action/storage_attestation","attest_author":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L/action/author_attestation","sign_citation":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L/action/citation_signature","submit_replication":"https://pith.science/pith/I3EZJJ44IOC7IKPISG5UBW6P4L/action/replication_record"}},"created_at":"2026-05-18T03:29:49.038751+00:00","updated_at":"2026-05-18T03:29:49.038751+00:00"}