{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SS3TJWG5EHM74OH24OVBUITCSP","short_pith_number":"pith:SS3TJWG5","schema_version":"1.0","canonical_sha256":"94b734d8dd21d9fe38fae3aa1a226293d4ba5fdb2791c435fe023c0f907b0bbe","source":{"kind":"arxiv","id":"1302.3657","version":2},"attestation_state":"computed","paper":{"title":"Some Remarks on Graphical Sequences for Graphs and Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Grant Cairns, Stacey Mendan","submitted_at":"2013-02-15T01:25:37Z","abstract_excerpt":"For finite sequence $\\underbar{\\em d}$ of positive integers, we consider graphs that have $\\underbar{\\em d}$ as their list of vertex degrees, and bipartite graphs for which each part has $\\underbar{\\em d}$ as its list of vertex degrees. In particular, we make a connection between a result for bipartite graphs by Alon, Ben-Shimon and Krivelevich and a result of Zverovich and Zverovich for graphs, and we give an improvement of a result of Zverovich and Zverovich. We show that the bipartite graphs with vertex degree sequences $(\\underbar{\\em d},\\underbar{\\em d}\\,)$ are in one to one correspondenc"},"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":"1302.3657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-15T01:25:37Z","cross_cats_sorted":[],"title_canon_sha256":"293ee7dbecd774e4a89ba73fe1d0ef9343468a8471a0acd57ffb71c8de7912fc","abstract_canon_sha256":"a6ba04d30f91117a2beaa4e13fb2c9686a49cb3254789783c5ad93d7d402d74b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:32.399354Z","signature_b64":"0wVajKsbbaH94b5Zs/JOo5DN20MP2L2JyFl4ddnGBhGjgxLXICRbB6G03+MCiNCgxwbxuaHkSnhu4ZrirgPeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94b734d8dd21d9fe38fae3aa1a226293d4ba5fdb2791c435fe023c0f907b0bbe","last_reissued_at":"2026-05-18T03:31:32.398707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:32.398707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Remarks on Graphical Sequences for Graphs and Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Grant Cairns, Stacey Mendan","submitted_at":"2013-02-15T01:25:37Z","abstract_excerpt":"For finite sequence $\\underbar{\\em d}$ of positive integers, we consider graphs that have $\\underbar{\\em d}$ as their list of vertex degrees, and bipartite graphs for which each part has $\\underbar{\\em d}$ as its list of vertex degrees. In particular, we make a connection between a result for bipartite graphs by Alon, Ben-Shimon and Krivelevich and a result of Zverovich and Zverovich for graphs, and we give an improvement of a result of Zverovich and Zverovich. We show that the bipartite graphs with vertex degree sequences $(\\underbar{\\em d},\\underbar{\\em d}\\,)$ are in one to one correspondenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3657","kind":"arxiv","version":2},"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":"1302.3657","created_at":"2026-05-18T03:31:32.398796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.3657v2","created_at":"2026-05-18T03:31:32.398796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3657","created_at":"2026-05-18T03:31:32.398796+00:00"},{"alias_kind":"pith_short_12","alias_value":"SS3TJWG5EHM7","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SS3TJWG5EHM74OH2","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SS3TJWG5","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/SS3TJWG5EHM74OH24OVBUITCSP","json":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP.json","graph_json":"https://pith.science/api/pith-number/SS3TJWG5EHM74OH24OVBUITCSP/graph.json","events_json":"https://pith.science/api/pith-number/SS3TJWG5EHM74OH24OVBUITCSP/events.json","paper":"https://pith.science/paper/SS3TJWG5"},"agent_actions":{"view_html":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP","download_json":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP.json","view_paper":"https://pith.science/paper/SS3TJWG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.3657&json=true","fetch_graph":"https://pith.science/api/pith-number/SS3TJWG5EHM74OH24OVBUITCSP/graph.json","fetch_events":"https://pith.science/api/pith-number/SS3TJWG5EHM74OH24OVBUITCSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP/action/storage_attestation","attest_author":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP/action/author_attestation","sign_citation":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP/action/citation_signature","submit_replication":"https://pith.science/pith/SS3TJWG5EHM74OH24OVBUITCSP/action/replication_record"}},"created_at":"2026-05-18T03:31:32.398796+00:00","updated_at":"2026-05-18T03:31:32.398796+00:00"}