{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7OGCAJ4UG4GPQVNXL4S3OPNYA4","short_pith_number":"pith:7OGCAJ4U","schema_version":"1.0","canonical_sha256":"fb8c202794370cf855b75f25b73db80738d1fde83139a12631380ccfa1c799ed","source":{"kind":"arxiv","id":"2407.05827","version":3},"attestation_state":"computed","paper":{"title":"An analogue of Reed's conjecture for digraphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta","submitted_at":"2024-07-08T11:14:41Z","abstract_excerpt":"Reed in 1998 conjectured that every graph $G$ satisfies $\\chi(G) \\leq \\lceil \\frac{\\Delta(G)+1+\\omega(G)}{2} \\rceil$. As a partial result, he proved the existence of $\\varepsilon > 0$ for which every graph $G$ satisfies $\\chi(G) \\leq \\lceil (1-\\varepsilon)(\\Delta(G)+1)+\\varepsilon\\omega(G) \\rceil$. We propose an analogue conjecture for digraphs. Given a digraph $D$, we denote by $\\vec{\\chi}(D)$ the dichromatic number of $D$, which is the minimum number of colours needed to partition $D$ into acyclic induced subdigraphs. We let $\\overleftrightarrow{\\omega}(D)$ denote the size of the largest bic"},"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":"2407.05827","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-08T11:14:41Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c788dffa6ab0dce886af443cca6c7eccd4f5eea57945f6aa1678f27e14d0d2c9","abstract_canon_sha256":"f86cd652b121a83337cc092c72e451aecc46dcee765c4fd344310966df5ba8b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:52.718592Z","signature_b64":"LafrjZFxE4pwlsstvhcOMkj5jB4ghOy+BHAaR9c3/wx5cKI95SQ1ji/Il+Z6fHREDhU7mqqfOG7Wph+d0807BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb8c202794370cf855b75f25b73db80738d1fde83139a12631380ccfa1c799ed","last_reissued_at":"2026-07-05T11:59:52.718119Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:52.718119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An analogue of Reed's conjecture for digraphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta","submitted_at":"2024-07-08T11:14:41Z","abstract_excerpt":"Reed in 1998 conjectured that every graph $G$ satisfies $\\chi(G) \\leq \\lceil \\frac{\\Delta(G)+1+\\omega(G)}{2} \\rceil$. As a partial result, he proved the existence of $\\varepsilon > 0$ for which every graph $G$ satisfies $\\chi(G) \\leq \\lceil (1-\\varepsilon)(\\Delta(G)+1)+\\varepsilon\\omega(G) \\rceil$. We propose an analogue conjecture for digraphs. Given a digraph $D$, we denote by $\\vec{\\chi}(D)$ the dichromatic number of $D$, which is the minimum number of colours needed to partition $D$ into acyclic induced subdigraphs. We let $\\overleftrightarrow{\\omega}(D)$ denote the size of the largest bic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05827","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/2407.05827/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":"2407.05827","created_at":"2026-07-05T11:59:52.718185+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.05827v3","created_at":"2026-07-05T11:59:52.718185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05827","created_at":"2026-07-05T11:59:52.718185+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OGCAJ4UG4GP","created_at":"2026-07-05T11:59:52.718185+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OGCAJ4UG4GPQVNX","created_at":"2026-07-05T11:59:52.718185+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OGCAJ4U","created_at":"2026-07-05T11:59:52.718185+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06928","citing_title":"Coloring digraphs with $\\Delta-b$ colors","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4","json":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4.json","graph_json":"https://pith.science/api/pith-number/7OGCAJ4UG4GPQVNXL4S3OPNYA4/graph.json","events_json":"https://pith.science/api/pith-number/7OGCAJ4UG4GPQVNXL4S3OPNYA4/events.json","paper":"https://pith.science/paper/7OGCAJ4U"},"agent_actions":{"view_html":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4","download_json":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4.json","view_paper":"https://pith.science/paper/7OGCAJ4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.05827&json=true","fetch_graph":"https://pith.science/api/pith-number/7OGCAJ4UG4GPQVNXL4S3OPNYA4/graph.json","fetch_events":"https://pith.science/api/pith-number/7OGCAJ4UG4GPQVNXL4S3OPNYA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4/action/storage_attestation","attest_author":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4/action/author_attestation","sign_citation":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4/action/citation_signature","submit_replication":"https://pith.science/pith/7OGCAJ4UG4GPQVNXL4S3OPNYA4/action/replication_record"}},"created_at":"2026-07-05T11:59:52.718185+00:00","updated_at":"2026-07-05T11:59:52.718185+00:00"}