{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Z26X2JSDQOMXMHJXTXV6WC373Y","short_pith_number":"pith:Z26X2JSD","schema_version":"1.0","canonical_sha256":"cebd7d26438399761d379debeb0b7fde06414175f26f0271d0464dd44eb61b56","source":{"kind":"arxiv","id":"2407.01625","version":2},"attestation_state":"computed","paper":{"title":"Balanced clique subdivisions and cycles lengths in $K_{s, t}$-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Fan Yang, Jianfeng Hou, Yindong Jin","submitted_at":"2024-06-29T06:25:18Z","abstract_excerpt":"Let $ t\\ge s\\ge2$ be integers. Confirming a conjecture of Mader, Liu and Montgomery [J. Lond. Math. Soc., 2017] showed that every $K_{s, t}$-free graph with average degree $d$ contains a subdivision of a clique with at least $\\Omega(d^{\\frac{s}{2(s-1)}})$ vertices. We give an improvement by showing that such a graph contains a balanced subdivision of a clique with the same order, where a balanced subdivision is a subdivision in which each edge is subdivided the same number of times.\n  In 1975, Erd\\H{o}s asked whether the sum of the reciprocals of the cycle lengths in a graph with infinite aver"},"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":"2407.01625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-29T06:25:18Z","cross_cats_sorted":[],"title_canon_sha256":"4e0487bd24cce6512bee30d4c5a7ea24b433c5399616d0aea909c84de406ea74","abstract_canon_sha256":"e79f6bc56758169711d262170ebe9f4aa17f69ac45f6e379960aee090e1fe27a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:15.707087Z","signature_b64":"EqEhdWzGKkOwyBvXkR+orL80L6vlufXWFQfGIMAbvrBr3sXvX80w94lbuguIjo6xBGWnEXABRQl0kjyTvtWgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cebd7d26438399761d379debeb0b7fde06414175f26f0271d0464dd44eb61b56","last_reissued_at":"2026-05-20T00:00:15.706425Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:15.706425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Balanced clique subdivisions and cycles lengths in $K_{s, t}$-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Fan Yang, Jianfeng Hou, Yindong Jin","submitted_at":"2024-06-29T06:25:18Z","abstract_excerpt":"Let $ t\\ge s\\ge2$ be integers. Confirming a conjecture of Mader, Liu and Montgomery [J. Lond. Math. Soc., 2017] showed that every $K_{s, t}$-free graph with average degree $d$ contains a subdivision of a clique with at least $\\Omega(d^{\\frac{s}{2(s-1)}})$ vertices. We give an improvement by showing that such a graph contains a balanced subdivision of a clique with the same order, where a balanced subdivision is a subdivision in which each edge is subdivided the same number of times.\n  In 1975, Erd\\H{o}s asked whether the sum of the reciprocals of the cycle lengths in a graph with infinite aver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01625","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.01625/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2407.01625","created_at":"2026-05-20T00:00:15.706520+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.01625v2","created_at":"2026-05-20T00:00:15.706520+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01625","created_at":"2026-05-20T00:00:15.706520+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z26X2JSDQOMX","created_at":"2026-05-20T00:00:15.706520+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z26X2JSDQOMXMHJX","created_at":"2026-05-20T00:00:15.706520+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z26X2JSD","created_at":"2026-05-20T00:00:15.706520+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/Z26X2JSDQOMXMHJXTXV6WC373Y","json":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y.json","graph_json":"https://pith.science/api/pith-number/Z26X2JSDQOMXMHJXTXV6WC373Y/graph.json","events_json":"https://pith.science/api/pith-number/Z26X2JSDQOMXMHJXTXV6WC373Y/events.json","paper":"https://pith.science/paper/Z26X2JSD"},"agent_actions":{"view_html":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y","download_json":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y.json","view_paper":"https://pith.science/paper/Z26X2JSD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.01625&json=true","fetch_graph":"https://pith.science/api/pith-number/Z26X2JSDQOMXMHJXTXV6WC373Y/graph.json","fetch_events":"https://pith.science/api/pith-number/Z26X2JSDQOMXMHJXTXV6WC373Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y/action/storage_attestation","attest_author":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y/action/author_attestation","sign_citation":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y/action/citation_signature","submit_replication":"https://pith.science/pith/Z26X2JSDQOMXMHJXTXV6WC373Y/action/replication_record"}},"created_at":"2026-05-20T00:00:15.706520+00:00","updated_at":"2026-05-20T00:00:15.706520+00:00"}