{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TMIHM6UWZVFNKMA4UB44VCTJKO","short_pith_number":"pith:TMIHM6UW","schema_version":"1.0","canonical_sha256":"9b10767a96cd4ad5301ca079ca8a6953b4602c6972bca5856b43d8d17e4fab3a","source":{"kind":"arxiv","id":"1709.03901","version":2},"attestation_state":"computed","paper":{"title":"Local resilience of an almost spanning $k$-cycle in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Milo\\v{s} Truji\\'c, Nemanja \\v{S}kori\\'c","submitted_at":"2017-09-12T15:12:22Z","abstract_excerpt":"The famous P\\'{o}sa-Seymour conjecture, confirmed in 1998 by Koml\\'{o}s, S\\'{a}rk\\\"{o}zy, and Szemer\\'{e}di, states that for any $k \\geq 2$, every graph on $n$ vertices with minimum degree $kn/(k + 1)$ contains the $k$-th power of a Hamilton cycle. We extend this result to a sparse random setting.\n  We show that for every $k \\geq 2$ there exists $C > 0$ such that if $p \\geq C(\\log n/n)^{1/k}$ then w.h.p. every subgraph of a random graph $G_{n, p}$ with minimum degree at least $(k/(k + 1) + o(1))np$, contains the $k$-th power of a cycle on at least $(1 - o(1))n$ vertices, improving upon the rec"},"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":"1709.03901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-12T15:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"be93eca95404d1b290d86fb42554a7e29b2feae7de23ae817b5adfd9a49b5641","abstract_canon_sha256":"44fe77cf12c60fa7e8652e735bdf198e8cbc788ceba2100dbc0081afc9b3523a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:51.134953Z","signature_b64":"Lsqr5MSIezCQ8fXyGzdZIJOeTJ1Sn2d5AuHJv/2RSGHwGru9Ff8JEIBonPRzuTWIMqkcNHcPNyhhtvTTFpa8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b10767a96cd4ad5301ca079ca8a6953b4602c6972bca5856b43d8d17e4fab3a","last_reissued_at":"2026-05-18T00:06:51.134367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:51.134367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local resilience of an almost spanning $k$-cycle in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Milo\\v{s} Truji\\'c, Nemanja \\v{S}kori\\'c","submitted_at":"2017-09-12T15:12:22Z","abstract_excerpt":"The famous P\\'{o}sa-Seymour conjecture, confirmed in 1998 by Koml\\'{o}s, S\\'{a}rk\\\"{o}zy, and Szemer\\'{e}di, states that for any $k \\geq 2$, every graph on $n$ vertices with minimum degree $kn/(k + 1)$ contains the $k$-th power of a Hamilton cycle. We extend this result to a sparse random setting.\n  We show that for every $k \\geq 2$ there exists $C > 0$ such that if $p \\geq C(\\log n/n)^{1/k}$ then w.h.p. every subgraph of a random graph $G_{n, p}$ with minimum degree at least $(k/(k + 1) + o(1))np$, contains the $k$-th power of a cycle on at least $(1 - o(1))n$ vertices, improving upon the rec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03901","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":"1709.03901","created_at":"2026-05-18T00:06:51.134455+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.03901v2","created_at":"2026-05-18T00:06:51.134455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03901","created_at":"2026-05-18T00:06:51.134455+00:00"},{"alias_kind":"pith_short_12","alias_value":"TMIHM6UWZVFN","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TMIHM6UWZVFNKMA4","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TMIHM6UW","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/TMIHM6UWZVFNKMA4UB44VCTJKO","json":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO.json","graph_json":"https://pith.science/api/pith-number/TMIHM6UWZVFNKMA4UB44VCTJKO/graph.json","events_json":"https://pith.science/api/pith-number/TMIHM6UWZVFNKMA4UB44VCTJKO/events.json","paper":"https://pith.science/paper/TMIHM6UW"},"agent_actions":{"view_html":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO","download_json":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO.json","view_paper":"https://pith.science/paper/TMIHM6UW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.03901&json=true","fetch_graph":"https://pith.science/api/pith-number/TMIHM6UWZVFNKMA4UB44VCTJKO/graph.json","fetch_events":"https://pith.science/api/pith-number/TMIHM6UWZVFNKMA4UB44VCTJKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO/action/storage_attestation","attest_author":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO/action/author_attestation","sign_citation":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO/action/citation_signature","submit_replication":"https://pith.science/pith/TMIHM6UWZVFNKMA4UB44VCTJKO/action/replication_record"}},"created_at":"2026-05-18T00:06:51.134455+00:00","updated_at":"2026-05-18T00:06:51.134455+00:00"}