{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I4O3CLWASDDY5TVS5DFEO76TU2","short_pith_number":"pith:I4O3CLWA","schema_version":"1.0","canonical_sha256":"471db12ec090c78eceb2e8ca477fd3a69b72b98d1811b941653cc73ded1f1765","source":{"kind":"arxiv","id":"1109.3741","version":1},"attestation_state":"computed","paper":{"title":"Immersing complete digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bojan Mohar, Diego Scheide, Jessica McDonald, Matt DeVos","submitted_at":"2011-09-17T00:59:26Z","abstract_excerpt":"We consider the problem of immersing the complete digraph on t vertices in a simple digraph. For Eulerian digraphs, we show that such an immersion always exists whenever minimum degree is at least t(t-1), and for t at most 4 minimum degree at least t-1 suffices. On the other hand, we show that there exist non-Eulerian digraphs with all vertices of arbitrarily high in- and outdegree which do not contain an immersion of the complete digraph on 3 vertices. As a side result, we obtain a construction of digraphs with large outdegree in which all cycles have odd length, simplifying a former construc"},"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":"1109.3741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-17T00:59:26Z","cross_cats_sorted":[],"title_canon_sha256":"8b2afca381790f9be917c02433c3b8123e2c704827f2947ea0a7e82e8673b4c7","abstract_canon_sha256":"25d5365441ac956c608db58b9b7ae5a41d5d0434db33fff2e2d664d8de691ae3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:45.990578Z","signature_b64":"uEr578iTzN98uSVbEs07Wl4d+0K2F37cWLK+NnwzrjMXgv+9Ur3w6sKTmdeyoVDWTbkaSs5my0vXwTTMelEcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"471db12ec090c78eceb2e8ca477fd3a69b72b98d1811b941653cc73ded1f1765","last_reissued_at":"2026-05-18T04:12:45.989920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:45.989920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Immersing complete digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bojan Mohar, Diego Scheide, Jessica McDonald, Matt DeVos","submitted_at":"2011-09-17T00:59:26Z","abstract_excerpt":"We consider the problem of immersing the complete digraph on t vertices in a simple digraph. For Eulerian digraphs, we show that such an immersion always exists whenever minimum degree is at least t(t-1), and for t at most 4 minimum degree at least t-1 suffices. On the other hand, we show that there exist non-Eulerian digraphs with all vertices of arbitrarily high in- and outdegree which do not contain an immersion of the complete digraph on 3 vertices. As a side result, we obtain a construction of digraphs with large outdegree in which all cycles have odd length, simplifying a former construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3741","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":"1109.3741","created_at":"2026-05-18T04:12:45.990015+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.3741v1","created_at":"2026-05-18T04:12:45.990015+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3741","created_at":"2026-05-18T04:12:45.990015+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4O3CLWASDDY","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4O3CLWASDDY5TVS","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4O3CLWA","created_at":"2026-05-18T12:26:30.835961+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/I4O3CLWASDDY5TVS5DFEO76TU2","json":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2.json","graph_json":"https://pith.science/api/pith-number/I4O3CLWASDDY5TVS5DFEO76TU2/graph.json","events_json":"https://pith.science/api/pith-number/I4O3CLWASDDY5TVS5DFEO76TU2/events.json","paper":"https://pith.science/paper/I4O3CLWA"},"agent_actions":{"view_html":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2","download_json":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2.json","view_paper":"https://pith.science/paper/I4O3CLWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.3741&json=true","fetch_graph":"https://pith.science/api/pith-number/I4O3CLWASDDY5TVS5DFEO76TU2/graph.json","fetch_events":"https://pith.science/api/pith-number/I4O3CLWASDDY5TVS5DFEO76TU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2/action/storage_attestation","attest_author":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2/action/author_attestation","sign_citation":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2/action/citation_signature","submit_replication":"https://pith.science/pith/I4O3CLWASDDY5TVS5DFEO76TU2/action/replication_record"}},"created_at":"2026-05-18T04:12:45.990015+00:00","updated_at":"2026-05-18T04:12:45.990015+00:00"}