{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EMDFBFLOJDZGEKVGB2VOITJP2W","short_pith_number":"pith:EMDFBFLO","schema_version":"1.0","canonical_sha256":"230650956e48f2622aa60eaae44d2fd5a4a4c6311d6d60d4fc4080f6f460a0bf","source":{"kind":"arxiv","id":"1202.2602","version":1},"attestation_state":"computed","paper":{"title":"Large feedback arc sets, high minimum degree subgraphs, and long cycles in Eulerian digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Shapira, Benny Sudakov, Hao Huang, Jie Ma, Raphael Yuster","submitted_at":"2012-02-13T01:47:29Z","abstract_excerpt":"A minimum feedback arc set of a directed graph $G$ is a smallest set of arcs whose removal makes $G$ acyclic. Its cardinality is denoted by $\\beta(G)$. We show that an Eulerian digraph with $n$ vertices and $m$ arcs has $\\beta(G) \\ge m^2/2n^2+m/2n$, and this bound is optimal for infinitely many $m, n$. Using this result we prove that an Eulerian digraph contains a cycle of length at most $6n^2/m$, and has an Eulerian subgraph with minimum degree at least $m^2/24n^3$. Both estimates are tight up to a constant factor. Finally, motivated by a conjecture of Bollob\\'as and Scott, we also show how t"},"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":"1202.2602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-13T01:47:29Z","cross_cats_sorted":[],"title_canon_sha256":"d38b06193ea7a4219b7ca8098e0f7e7512209890041293bb8a48a7701747a3f3","abstract_canon_sha256":"dc4cb2a96621fd5c44e264b887dc85045fe20dfbc4793acb178bab26d6064f92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:26.125546Z","signature_b64":"EhwCCDNmak2p7t1QEt1FU+seJHNHXAHLsA6eyQRVzXv4khiqLDvM92l+45/YnImSsyC730Rfk9YJzYwiI55uBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230650956e48f2622aa60eaae44d2fd5a4a4c6311d6d60d4fc4080f6f460a0bf","last_reissued_at":"2026-05-18T04:02:26.124953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:26.124953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large feedback arc sets, high minimum degree subgraphs, and long cycles in Eulerian digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Shapira, Benny Sudakov, Hao Huang, Jie Ma, Raphael Yuster","submitted_at":"2012-02-13T01:47:29Z","abstract_excerpt":"A minimum feedback arc set of a directed graph $G$ is a smallest set of arcs whose removal makes $G$ acyclic. Its cardinality is denoted by $\\beta(G)$. We show that an Eulerian digraph with $n$ vertices and $m$ arcs has $\\beta(G) \\ge m^2/2n^2+m/2n$, and this bound is optimal for infinitely many $m, n$. Using this result we prove that an Eulerian digraph contains a cycle of length at most $6n^2/m$, and has an Eulerian subgraph with minimum degree at least $m^2/24n^3$. Both estimates are tight up to a constant factor. Finally, motivated by a conjecture of Bollob\\'as and Scott, we also show how t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2602","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":"1202.2602","created_at":"2026-05-18T04:02:26.125029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2602v1","created_at":"2026-05-18T04:02:26.125029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2602","created_at":"2026-05-18T04:02:26.125029+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMDFBFLOJDZG","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMDFBFLOJDZGEKVG","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMDFBFLO","created_at":"2026-05-18T12:27:04.183437+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/EMDFBFLOJDZGEKVGB2VOITJP2W","json":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W.json","graph_json":"https://pith.science/api/pith-number/EMDFBFLOJDZGEKVGB2VOITJP2W/graph.json","events_json":"https://pith.science/api/pith-number/EMDFBFLOJDZGEKVGB2VOITJP2W/events.json","paper":"https://pith.science/paper/EMDFBFLO"},"agent_actions":{"view_html":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W","download_json":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W.json","view_paper":"https://pith.science/paper/EMDFBFLO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2602&json=true","fetch_graph":"https://pith.science/api/pith-number/EMDFBFLOJDZGEKVGB2VOITJP2W/graph.json","fetch_events":"https://pith.science/api/pith-number/EMDFBFLOJDZGEKVGB2VOITJP2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W/action/storage_attestation","attest_author":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W/action/author_attestation","sign_citation":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W/action/citation_signature","submit_replication":"https://pith.science/pith/EMDFBFLOJDZGEKVGB2VOITJP2W/action/replication_record"}},"created_at":"2026-05-18T04:02:26.125029+00:00","updated_at":"2026-05-18T04:02:26.125029+00:00"}