{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ECPHSAK344C3KIDEQFVPC2BVUZ","short_pith_number":"pith:ECPHSAK3","schema_version":"1.0","canonical_sha256":"209e79015be705b52064816af16835a660b8982dd63a5fdb073b96358ff520b6","source":{"kind":"arxiv","id":"2303.05505","version":2},"attestation_state":"computed","paper":{"title":"On interval colourings of graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Julien Portier, Lawrence Hollom, Leo Versteegen","submitted_at":"2023-03-09T18:56:26Z","abstract_excerpt":"An interval colouring of a graph $G=(V,E)$ is a proper colouring $c\\colon E\\to \\mathbb{Z}$ such that the set of colours of edges incident to any given vertex forms an interval of $\\mathbb{Z}$. The interval thickness $\\theta(G)$ of a graph $G$ is the smallest integer $k$ such that $G$ can be edge-partitioned into $k$ interval colourable graphs, and $\\theta(n)$ is the largest interval thickness over graphs on $n$ vertices. We show that $c \\frac{\\log n}{\\log \\log n} \\leq \\theta(n) \\leq n^{8/9+o(1)}$ for some $c>0$. In particular this answers a question by Asratian, Casselgren, and Petrosyan.\n  In"},"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":"2303.05505","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-03-09T18:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"2f72e865ee266799e729e6183e480fc9910bbffe3c42362ced34ac552f50e431","abstract_canon_sha256":"2e0b50e7ca89a4004c0ca007e7b7f4956c56ecba1a16a67420dc738368e3092d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:14:41.600431Z","signature_b64":"G5GpZbDy7BTKXRZmUqYCYIG+V22OGxF6P1n7ujlLP9cyqj3KYKhlz9xHNKtcZYNoAACBay/Gx5MMcHQw8Q/zDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"209e79015be705b52064816af16835a660b8982dd63a5fdb073b96358ff520b6","last_reissued_at":"2026-07-05T06:14:41.599730Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:14:41.599730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On interval colourings of graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Julien Portier, Lawrence Hollom, Leo Versteegen","submitted_at":"2023-03-09T18:56:26Z","abstract_excerpt":"An interval colouring of a graph $G=(V,E)$ is a proper colouring $c\\colon E\\to \\mathbb{Z}$ such that the set of colours of edges incident to any given vertex forms an interval of $\\mathbb{Z}$. The interval thickness $\\theta(G)$ of a graph $G$ is the smallest integer $k$ such that $G$ can be edge-partitioned into $k$ interval colourable graphs, and $\\theta(n)$ is the largest interval thickness over graphs on $n$ vertices. We show that $c \\frac{\\log n}{\\log \\log n} \\leq \\theta(n) \\leq n^{8/9+o(1)}$ for some $c>0$. In particular this answers a question by Asratian, Casselgren, and Petrosyan.\n  In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.05505","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/2303.05505/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":"2303.05505","created_at":"2026-07-05T06:14:41.599802+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.05505v2","created_at":"2026-07-05T06:14:41.599802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.05505","created_at":"2026-07-05T06:14:41.599802+00:00"},{"alias_kind":"pith_short_12","alias_value":"ECPHSAK344C3","created_at":"2026-07-05T06:14:41.599802+00:00"},{"alias_kind":"pith_short_16","alias_value":"ECPHSAK344C3KIDE","created_at":"2026-07-05T06:14:41.599802+00:00"},{"alias_kind":"pith_short_8","alias_value":"ECPHSAK3","created_at":"2026-07-05T06:14:41.599802+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/ECPHSAK344C3KIDEQFVPC2BVUZ","json":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ.json","graph_json":"https://pith.science/api/pith-number/ECPHSAK344C3KIDEQFVPC2BVUZ/graph.json","events_json":"https://pith.science/api/pith-number/ECPHSAK344C3KIDEQFVPC2BVUZ/events.json","paper":"https://pith.science/paper/ECPHSAK3"},"agent_actions":{"view_html":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ","download_json":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ.json","view_paper":"https://pith.science/paper/ECPHSAK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.05505&json=true","fetch_graph":"https://pith.science/api/pith-number/ECPHSAK344C3KIDEQFVPC2BVUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ECPHSAK344C3KIDEQFVPC2BVUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ/action/storage_attestation","attest_author":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ/action/author_attestation","sign_citation":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ/action/citation_signature","submit_replication":"https://pith.science/pith/ECPHSAK344C3KIDEQFVPC2BVUZ/action/replication_record"}},"created_at":"2026-07-05T06:14:41.599802+00:00","updated_at":"2026-07-05T06:14:41.599802+00:00"}