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We prove that the following edge variant of the Erd{\\H o}s-P{\\'o}sa property holds for every $r\\geq 2$: if $G$ is a graph and $k$ is a positive integer, then either $G$ contains a packing of $k$ mutually edge-disjoint models of $\\theta_{r}$, or it contains a set $S$ of $f_r(k)$ edges such that $G\\setminus S$ has no $\\theta_{r}$-model, for both $f_r(k) "},"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":"1311.1108","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-05T16:13:28Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b68aaefd535f3ea328b6adc0556cdd93ee57df331fff5878db03b6992fb264e1","abstract_canon_sha256":"e5ac7e6c50bb42d34ff9b3c76ef0e41c7d558de987395eb9331cca5ee83f3010"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:06.998772Z","signature_b64":"dNZE6+d6hYsSRKkqtYbJNeMAoIPxtODpl5E3ZU9q/suHCvuiIBZT5DBgq0y9qAHb78v54lBrER+Dx3tuaRniDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96ccd0d9570565a5cf8e96ef89ea99fa3d11a0aa2316f25348488963eaa2f375","last_reissued_at":"2026-05-18T01:33:06.998346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:06.998346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An edge variant of the Erd\\H{o}s-P\\'osa property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Dimitrios M. 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We prove that the following edge variant of the Erd{\\H o}s-P{\\'o}sa property holds for every $r\\geq 2$: if $G$ is a graph and $k$ is a positive integer, then either $G$ contains a packing of $k$ mutually edge-disjoint models of $\\theta_{r}$, or it contains a set $S$ of $f_r(k)$ edges such that $G\\setminus S$ has no $\\theta_{r}$-model, for both $f_r(k) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1108","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.1108","created_at":"2026-05-18T01:33:06.998412+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.1108v3","created_at":"2026-05-18T01:33:06.998412+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1108","created_at":"2026-05-18T01:33:06.998412+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3GNBWKXAVS2","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3GNBWKXAVS2LT4O","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3GNBWKX","created_at":"2026-05-18T12:27:59.945178+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/S3GNBWKXAVS2LT4OS3XYT2UZ7I","json":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I.json","graph_json":"https://pith.science/api/pith-number/S3GNBWKXAVS2LT4OS3XYT2UZ7I/graph.json","events_json":"https://pith.science/api/pith-number/S3GNBWKXAVS2LT4OS3XYT2UZ7I/events.json","paper":"https://pith.science/paper/S3GNBWKX"},"agent_actions":{"view_html":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I","download_json":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I.json","view_paper":"https://pith.science/paper/S3GNBWKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.1108&json=true","fetch_graph":"https://pith.science/api/pith-number/S3GNBWKXAVS2LT4OS3XYT2UZ7I/graph.json","fetch_events":"https://pith.science/api/pith-number/S3GNBWKXAVS2LT4OS3XYT2UZ7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I/action/storage_attestation","attest_author":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I/action/author_attestation","sign_citation":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I/action/citation_signature","submit_replication":"https://pith.science/pith/S3GNBWKXAVS2LT4OS3XYT2UZ7I/action/replication_record"}},"created_at":"2026-05-18T01:33:06.998412+00:00","updated_at":"2026-05-18T01:33:06.998412+00:00"}