{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Q36OCKS3U5LD5N6IKE4KFJYQNX","short_pith_number":"pith:Q36OCKS3","schema_version":"1.0","canonical_sha256":"86fce12a5ba7563eb7c85138a2a7106df585a98bb88f994d998163bd556dc56f","source":{"kind":"arxiv","id":"1905.02856","version":3},"attestation_state":"computed","paper":{"title":"Max-Cut in Degenerate $H$-Free Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Nitya Mani, Ray Li","submitted_at":"2019-05-08T01:04:42Z","abstract_excerpt":"We obtain several lower bounds on the $\\textsf{Max-Cut}$ of $d$-degenerate $H$-free graphs. Let $f(m,d,H)$ denote the smallest $\\textsf{Max-Cut}$ of an $H$-free $d$-degenerate graph on $m$ edges. We show that $f(m,d,K_r)\\ge \\left(\\frac{1}{2} + d^{-1+\\Omega(r^{-1})}\\right)m$, generalizing a recent work of Carlson, Kolla, and Trevisan. We also give bounds on $f(m,d,H)$ when $H$ is a cycle, odd wheel, or a complete bipartite graph with at most 4 vertices on one side. We also show stronger bounds on $f(m,d,K_r)$ assuming a conjecture of Alon, Bollabas, Krivelevich, and Sudakov (2003). We conjectur"},"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":"1905.02856","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-08T01:04:42Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"7b86bd04f7db326e2ebd76599cc358f2d6cf602c5ecc048c5ad039398052b39e","abstract_canon_sha256":"dfb848522f3f50dbae914d04428664dbfcff04d1ac3eed0fbca61b7e606ee510"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:58:02.880772Z","signature_b64":"g/dy1o5xf7D2x7XMgbUyzS3HS+Rlbt1FIcPQ7o6Qf3VMasX7G80K16XWTpEVEBg1lNQikrHyLBE8tFx+Ui5bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86fce12a5ba7563eb7c85138a2a7106df585a98bb88f994d998163bd556dc56f","last_reissued_at":"2026-07-05T00:58:02.880275Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:58:02.880275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Max-Cut in Degenerate $H$-Free Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Nitya Mani, Ray Li","submitted_at":"2019-05-08T01:04:42Z","abstract_excerpt":"We obtain several lower bounds on the $\\textsf{Max-Cut}$ of $d$-degenerate $H$-free graphs. Let $f(m,d,H)$ denote the smallest $\\textsf{Max-Cut}$ of an $H$-free $d$-degenerate graph on $m$ edges. We show that $f(m,d,K_r)\\ge \\left(\\frac{1}{2} + d^{-1+\\Omega(r^{-1})}\\right)m$, generalizing a recent work of Carlson, Kolla, and Trevisan. We also give bounds on $f(m,d,H)$ when $H$ is a cycle, odd wheel, or a complete bipartite graph with at most 4 vertices on one side. We also show stronger bounds on $f(m,d,K_r)$ assuming a conjecture of Alon, Bollabas, Krivelevich, and Sudakov (2003). We conjectur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02856","kind":"arxiv","version":3},"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/1905.02856/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":"1905.02856","created_at":"2026-07-05T00:58:02.880344+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.02856v3","created_at":"2026-07-05T00:58:02.880344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02856","created_at":"2026-07-05T00:58:02.880344+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q36OCKS3U5LD","created_at":"2026-07-05T00:58:02.880344+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q36OCKS3U5LD5N6I","created_at":"2026-07-05T00:58:02.880344+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q36OCKS3","created_at":"2026-07-05T00:58:02.880344+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/Q36OCKS3U5LD5N6IKE4KFJYQNX","json":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX.json","graph_json":"https://pith.science/api/pith-number/Q36OCKS3U5LD5N6IKE4KFJYQNX/graph.json","events_json":"https://pith.science/api/pith-number/Q36OCKS3U5LD5N6IKE4KFJYQNX/events.json","paper":"https://pith.science/paper/Q36OCKS3"},"agent_actions":{"view_html":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX","download_json":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX.json","view_paper":"https://pith.science/paper/Q36OCKS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.02856&json=true","fetch_graph":"https://pith.science/api/pith-number/Q36OCKS3U5LD5N6IKE4KFJYQNX/graph.json","fetch_events":"https://pith.science/api/pith-number/Q36OCKS3U5LD5N6IKE4KFJYQNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX/action/storage_attestation","attest_author":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX/action/author_attestation","sign_citation":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX/action/citation_signature","submit_replication":"https://pith.science/pith/Q36OCKS3U5LD5N6IKE4KFJYQNX/action/replication_record"}},"created_at":"2026-07-05T00:58:02.880344+00:00","updated_at":"2026-07-05T00:58:02.880344+00:00"}