{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VERXVQQFSWKZX4OGJI6MYKP7V5","short_pith_number":"pith:VERXVQQF","schema_version":"1.0","canonical_sha256":"a9237ac20595959bf1c64a3ccc29ffaf5917727aa7a58b3dbd83bdb3cf5b0938","source":{"kind":"arxiv","id":"1206.3945","version":3},"attestation_state":"computed","paper":{"title":"List-coloring graphs on surfaces with varying list-sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice M. Dean, Joan P. Hutchinson","submitted_at":"2012-06-18T14:22:08Z","abstract_excerpt":"Let $G$ be a graph embedded on a surface $S_\\varepsilon$ with Euler genus $\\varepsilon > 0$, and let $P\\subseteq V(G)$ be a set of vertices mutually at distance at least 4 apart. Suppose all vertices of $G$ have $H(\\varepsilon)$-lists and the vertices of $P$ are precolored, where $H(\\varepsilon)=\\Big\\lfloor\\frac{7 + \\sqrt{24\\varepsilon + 1}}{2}\\Big\\rfloor$ is the Heawood number. We show that the coloring of $P$ extends to a list-coloring of $G$ and that the distance bound of 4 is best possible. Our result provides an answer to an analogous question of Albertson about extending a precoloring of"},"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":"1206.3945","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-18T14:22:08Z","cross_cats_sorted":[],"title_canon_sha256":"d41941723bc004c88fa88351758e9d44c900b3c5697c29c3af461416323bff78","abstract_canon_sha256":"0157453586960d9896c41f8c2a1343f6cf9d66e7729c6a014916d57c12825889"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:28.942717Z","signature_b64":"XaRFtSRAptZ72VFwQB0W9vlpv44c61rFdOLdr4xZAChFOvTnmBUUZFOJq4a5wYEur5pTjt/UA7O9MYmWUA11Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9237ac20595959bf1c64a3ccc29ffaf5917727aa7a58b3dbd83bdb3cf5b0938","last_reissued_at":"2026-05-18T03:37:28.942117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:28.942117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"List-coloring graphs on surfaces with varying list-sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice M. Dean, Joan P. Hutchinson","submitted_at":"2012-06-18T14:22:08Z","abstract_excerpt":"Let $G$ be a graph embedded on a surface $S_\\varepsilon$ with Euler genus $\\varepsilon > 0$, and let $P\\subseteq V(G)$ be a set of vertices mutually at distance at least 4 apart. Suppose all vertices of $G$ have $H(\\varepsilon)$-lists and the vertices of $P$ are precolored, where $H(\\varepsilon)=\\Big\\lfloor\\frac{7 + \\sqrt{24\\varepsilon + 1}}{2}\\Big\\rfloor$ is the Heawood number. We show that the coloring of $P$ extends to a list-coloring of $G$ and that the distance bound of 4 is best possible. Our result provides an answer to an analogous question of Albertson about extending a precoloring of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3945","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":""},"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":"1206.3945","created_at":"2026-05-18T03:37:28.942211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3945v3","created_at":"2026-05-18T03:37:28.942211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3945","created_at":"2026-05-18T03:37:28.942211+00:00"},{"alias_kind":"pith_short_12","alias_value":"VERXVQQFSWKZ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VERXVQQFSWKZX4OG","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VERXVQQF","created_at":"2026-05-18T12:27:25.539911+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/VERXVQQFSWKZX4OGJI6MYKP7V5","json":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5.json","graph_json":"https://pith.science/api/pith-number/VERXVQQFSWKZX4OGJI6MYKP7V5/graph.json","events_json":"https://pith.science/api/pith-number/VERXVQQFSWKZX4OGJI6MYKP7V5/events.json","paper":"https://pith.science/paper/VERXVQQF"},"agent_actions":{"view_html":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5","download_json":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5.json","view_paper":"https://pith.science/paper/VERXVQQF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3945&json=true","fetch_graph":"https://pith.science/api/pith-number/VERXVQQFSWKZX4OGJI6MYKP7V5/graph.json","fetch_events":"https://pith.science/api/pith-number/VERXVQQFSWKZX4OGJI6MYKP7V5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5/action/storage_attestation","attest_author":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5/action/author_attestation","sign_citation":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5/action/citation_signature","submit_replication":"https://pith.science/pith/VERXVQQFSWKZX4OGJI6MYKP7V5/action/replication_record"}},"created_at":"2026-05-18T03:37:28.942211+00:00","updated_at":"2026-05-18T03:37:28.942211+00:00"}