{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KH4DCGENK4FUL7Y3QEY4IDA2AK","short_pith_number":"pith:KH4DCGEN","schema_version":"1.0","canonical_sha256":"51f831188d570b45ff1b8131c40c1a028b4d11849d2316bce0aea71901a58842","source":{"kind":"arxiv","id":"1703.10268","version":2},"attestation_state":"computed","paper":{"title":"Extensions of a theorem of Erd\\H{o}s on nonhamiltonian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Ruth Luo, Zolt\\'an F\\\"uredi","submitted_at":"2017-03-29T23:28:47Z","abstract_excerpt":"Let $n, d$ be integers with $1 \\leq d \\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, and set $h(n,d):={n-d \\choose 2} + d^2$. Erd\\H{o}s proved that when $n \\geq 6d$, each nonhamiltonian graph $G$ on $n$ vertices with minimum degree $\\delta(G) \\geq d$ has at most $h(n,d)$ edges. He also provides a sharpness example $H_{n,d}$ for all such pairs $n,d$. Previously, we showed a stability version of this result: for $n$ large enough, every nonhamiltonian graph $G$ on $n$ vertices with $\\delta(G) \\geq d$ and more than $h(n,d+1)$ edges is a subgraph of $H_{n,d}$.\n  In this paper, we show that not o"},"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":"1703.10268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-29T23:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"3b58f55e19449852d21566962c71dc24408f0f5635565d363acd74eadb3ca11d","abstract_canon_sha256":"c0420c42c5467f533e0eac77d69eea1ff631943f445bf64fb46089c4488c1f92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:54.950784Z","signature_b64":"cAOYIQfUePKlXeNWLka5h5Q66iFgYc8Bf0t0a3l9ZapmO5me+9Gy3V7O6X9CwsZJ3taN5qzfblONSCSDPeJxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f831188d570b45ff1b8131c40c1a028b4d11849d2316bce0aea71901a58842","last_reissued_at":"2026-05-18T00:46:54.950154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:54.950154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of a theorem of Erd\\H{o}s on nonhamiltonian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Ruth Luo, Zolt\\'an F\\\"uredi","submitted_at":"2017-03-29T23:28:47Z","abstract_excerpt":"Let $n, d$ be integers with $1 \\leq d \\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, and set $h(n,d):={n-d \\choose 2} + d^2$. Erd\\H{o}s proved that when $n \\geq 6d$, each nonhamiltonian graph $G$ on $n$ vertices with minimum degree $\\delta(G) \\geq d$ has at most $h(n,d)$ edges. He also provides a sharpness example $H_{n,d}$ for all such pairs $n,d$. Previously, we showed a stability version of this result: for $n$ large enough, every nonhamiltonian graph $G$ on $n$ vertices with $\\delta(G) \\geq d$ and more than $h(n,d+1)$ edges is a subgraph of $H_{n,d}$.\n  In this paper, we show that not o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10268","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":"1703.10268","created_at":"2026-05-18T00:46:54.950240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10268v2","created_at":"2026-05-18T00:46:54.950240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10268","created_at":"2026-05-18T00:46:54.950240+00:00"},{"alias_kind":"pith_short_12","alias_value":"KH4DCGENK4FU","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KH4DCGENK4FUL7Y3","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KH4DCGEN","created_at":"2026-05-18T12:31:24.725408+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/KH4DCGENK4FUL7Y3QEY4IDA2AK","json":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK.json","graph_json":"https://pith.science/api/pith-number/KH4DCGENK4FUL7Y3QEY4IDA2AK/graph.json","events_json":"https://pith.science/api/pith-number/KH4DCGENK4FUL7Y3QEY4IDA2AK/events.json","paper":"https://pith.science/paper/KH4DCGEN"},"agent_actions":{"view_html":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK","download_json":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK.json","view_paper":"https://pith.science/paper/KH4DCGEN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10268&json=true","fetch_graph":"https://pith.science/api/pith-number/KH4DCGENK4FUL7Y3QEY4IDA2AK/graph.json","fetch_events":"https://pith.science/api/pith-number/KH4DCGENK4FUL7Y3QEY4IDA2AK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK/action/storage_attestation","attest_author":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK/action/author_attestation","sign_citation":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK/action/citation_signature","submit_replication":"https://pith.science/pith/KH4DCGENK4FUL7Y3QEY4IDA2AK/action/replication_record"}},"created_at":"2026-05-18T00:46:54.950240+00:00","updated_at":"2026-05-18T00:46:54.950240+00:00"}