{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZULGCPGR74I2FOKKKTUF2NJCKP","short_pith_number":"pith:ZULGCPGR","schema_version":"1.0","canonical_sha256":"cd16613cd1ff11a2b94a54e85d352253fe992b140b02ec442680349656610658","source":{"kind":"arxiv","id":"1708.05454","version":1},"attestation_state":"computed","paper":{"title":"On subgraphs of $C_{2k}$-free graphs and a problem of K\\\"uhn and Osthus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2017-08-17T22:43:55Z","abstract_excerpt":"Let $c$ denote the largest constant such that every $C_{6}$-free graph $G$ contains a bipartite and $C_4$-free subgraph having $c$ fraction of edges of $G$. Gy\\H{o}ri et al. showed that $\\frac{3}{8} \\le c \\le \\frac{2}{5}$. We prove that $c=\\frac{3}{8}$. More generally, we show that for any $\\varepsilon>0$, and any integer $k \\ge 2$, there is a $C_{2k}$-free graph $G_1$ which does not contain a bipartite subgraph of girth greater than $2k$ with more than $\\left(1-\\frac{1}{2^{2k-2}}\\right)\\frac{2}{2k-1}(1+\\varepsilon)$ fraction of the edges of $G_1$. There also exists a $C_{2k}$-free graph $G_2$"},"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":"1708.05454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-17T22:43:55Z","cross_cats_sorted":[],"title_canon_sha256":"b3153c4b55a1edcd7869fd9c10f2dbdc5d06bdbf89a01f61fe8ab1383702d5d3","abstract_canon_sha256":"0b7466b79fe6b8801571bdc8b35389f848e1f0eb39ddabbeac0de45a79484b57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:50.017674Z","signature_b64":"EzLqwz7L/86X8xM+1eb1mf0kskAt92SpPAvsaAj8ar8kFnk8/v9fItPcC87zyijLtcEo4QdUQEh4bFu6Ir6/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd16613cd1ff11a2b94a54e85d352253fe992b140b02ec442680349656610658","last_reissued_at":"2026-05-18T00:37:50.017196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:50.017196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On subgraphs of $C_{2k}$-free graphs and a problem of K\\\"uhn and Osthus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2017-08-17T22:43:55Z","abstract_excerpt":"Let $c$ denote the largest constant such that every $C_{6}$-free graph $G$ contains a bipartite and $C_4$-free subgraph having $c$ fraction of edges of $G$. Gy\\H{o}ri et al. showed that $\\frac{3}{8} \\le c \\le \\frac{2}{5}$. We prove that $c=\\frac{3}{8}$. More generally, we show that for any $\\varepsilon>0$, and any integer $k \\ge 2$, there is a $C_{2k}$-free graph $G_1$ which does not contain a bipartite subgraph of girth greater than $2k$ with more than $\\left(1-\\frac{1}{2^{2k-2}}\\right)\\frac{2}{2k-1}(1+\\varepsilon)$ fraction of the edges of $G_1$. There also exists a $C_{2k}$-free graph $G_2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05454","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":"1708.05454","created_at":"2026-05-18T00:37:50.017269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.05454v1","created_at":"2026-05-18T00:37:50.017269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05454","created_at":"2026-05-18T00:37:50.017269+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZULGCPGR74I2","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZULGCPGR74I2FOKK","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZULGCPGR","created_at":"2026-05-18T12:31:59.375834+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/ZULGCPGR74I2FOKKKTUF2NJCKP","json":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP.json","graph_json":"https://pith.science/api/pith-number/ZULGCPGR74I2FOKKKTUF2NJCKP/graph.json","events_json":"https://pith.science/api/pith-number/ZULGCPGR74I2FOKKKTUF2NJCKP/events.json","paper":"https://pith.science/paper/ZULGCPGR"},"agent_actions":{"view_html":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP","download_json":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP.json","view_paper":"https://pith.science/paper/ZULGCPGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.05454&json=true","fetch_graph":"https://pith.science/api/pith-number/ZULGCPGR74I2FOKKKTUF2NJCKP/graph.json","fetch_events":"https://pith.science/api/pith-number/ZULGCPGR74I2FOKKKTUF2NJCKP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP/action/storage_attestation","attest_author":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP/action/author_attestation","sign_citation":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP/action/citation_signature","submit_replication":"https://pith.science/pith/ZULGCPGR74I2FOKKKTUF2NJCKP/action/replication_record"}},"created_at":"2026-05-18T00:37:50.017269+00:00","updated_at":"2026-05-18T00:37:50.017269+00:00"}