{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TVJFCIH5VLMIQNGIWSVDTJQXA3","short_pith_number":"pith:TVJFCIH5","schema_version":"1.0","canonical_sha256":"9d525120fdaad88834c8b4aa39a61706cc932aae70346e04321adf1942df7b8a","source":{"kind":"arxiv","id":"1706.07274","version":1},"attestation_state":"computed","paper":{"title":"A note on edge degree and spanning trail containing given edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Baoyindureng Wu, Hong-Jian Lai, Weihua Yang","submitted_at":"2017-06-22T12:20:48Z","abstract_excerpt":"Let $G$ be a simple graph with $n\\geq4$ vertices and $d(x)+d(y)\\geq n+k$ for each edge $xy\\in E(G)$. In this work we prove that $G$ either contains a spanning closed trail containing any given edge set $X$ if $|X|\\leq k$, or $G$ is a well characterized graph. As a corollary, we show that line graphs of such graphs are $k$-hamiltonian."},"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":"1706.07274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-22T12:20:48Z","cross_cats_sorted":[],"title_canon_sha256":"e4f540f3ddbc87e613ccd49ba28975efd9cd76643f8a67a11476265596389d1f","abstract_canon_sha256":"6ccf3838ea8d53d18ea8fcc311af27b5b85f7d4141be8459138325ed797c6336"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:52.159511Z","signature_b64":"Nqr77J6PTPC9HsDFy7wA+8fml6ye2To/0MMgzdHRJjCe3o4zoR7Mwr/ZAImOvdt5jC4BC+qi4Nz5U3TGsXeaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d525120fdaad88834c8b4aa39a61706cc932aae70346e04321adf1942df7b8a","last_reissued_at":"2026-05-18T00:41:52.159019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:52.159019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on edge degree and spanning trail containing given edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Baoyindureng Wu, Hong-Jian Lai, Weihua Yang","submitted_at":"2017-06-22T12:20:48Z","abstract_excerpt":"Let $G$ be a simple graph with $n\\geq4$ vertices and $d(x)+d(y)\\geq n+k$ for each edge $xy\\in E(G)$. In this work we prove that $G$ either contains a spanning closed trail containing any given edge set $X$ if $|X|\\leq k$, or $G$ is a well characterized graph. As a corollary, we show that line graphs of such graphs are $k$-hamiltonian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07274","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":"1706.07274","created_at":"2026-05-18T00:41:52.159090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07274v1","created_at":"2026-05-18T00:41:52.159090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07274","created_at":"2026-05-18T00:41:52.159090+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVJFCIH5VLMI","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVJFCIH5VLMIQNGI","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVJFCIH5","created_at":"2026-05-18T12:31:46.661854+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/TVJFCIH5VLMIQNGIWSVDTJQXA3","json":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3.json","graph_json":"https://pith.science/api/pith-number/TVJFCIH5VLMIQNGIWSVDTJQXA3/graph.json","events_json":"https://pith.science/api/pith-number/TVJFCIH5VLMIQNGIWSVDTJQXA3/events.json","paper":"https://pith.science/paper/TVJFCIH5"},"agent_actions":{"view_html":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3","download_json":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3.json","view_paper":"https://pith.science/paper/TVJFCIH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07274&json=true","fetch_graph":"https://pith.science/api/pith-number/TVJFCIH5VLMIQNGIWSVDTJQXA3/graph.json","fetch_events":"https://pith.science/api/pith-number/TVJFCIH5VLMIQNGIWSVDTJQXA3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3/action/storage_attestation","attest_author":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3/action/author_attestation","sign_citation":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3/action/citation_signature","submit_replication":"https://pith.science/pith/TVJFCIH5VLMIQNGIWSVDTJQXA3/action/replication_record"}},"created_at":"2026-05-18T00:41:52.159090+00:00","updated_at":"2026-05-18T00:41:52.159090+00:00"}