{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JNGSZNBPCH6H56BFTTCXXVABGD","short_pith_number":"pith:JNGSZNBP","schema_version":"1.0","canonical_sha256":"4b4d2cb42f11fc7ef8259cc57bd40130c003b9099e3f4b515930dd402541210d","source":{"kind":"arxiv","id":"1302.2599","version":1},"attestation_state":"computed","paper":{"title":"$(3,1)^*$-choosability of planar graphs without adjacent short cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andre Raspaud, Min Chen","submitted_at":"2013-02-11T20:15:58Z","abstract_excerpt":"A list assignment of a graph $G$ is a function $L$ that assigns a list $L(v)$ of colors to each vertex $v\\in V(G)$. An $(L,d)^*$-coloring is a mapping $\\pi$ that assigns a color $\\pi(v)\\in L(v)$ to each vertex $v\\in V(G)$ so that at most $d$ neighbors of $v$ receive color $\\pi(v)$. A graph $G$ is said to be $(k,d)^*$-choosable if it admits an $(L,d)^*$-coloring for every list assignment $L$ with $|L(v)|\\ge k$ for all $v\\in V(G)$. In 2001, Lih et al. \\cite{LSWZ-01} proved that planar graphs without 4- and $l$-cycles are $(3,1)^*$-choosable, where $l\\in \\{5,6,7\\}$. Later, Dong and Xu \\cite{DX-09"},"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":"1302.2599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-11T20:15:58Z","cross_cats_sorted":[],"title_canon_sha256":"ecbd588eaeea40fcb0343ace21110ed01f96a7079ca5312a0122e845173e7ee1","abstract_canon_sha256":"e6b4eeecc6225c79b4d375a4c1c43a753d43da953532ba5429a40876e955b761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.667520Z","signature_b64":"ecNWAqezDInKVvWNKksrCI64AvuKan+lz+ln/EQmJe0fLQfX6T01+Or2Ld+bGeWHFe8n/NDSs1/p1wIDjq19BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b4d2cb42f11fc7ef8259cc57bd40130c003b9099e3f4b515930dd402541210d","last_reissued_at":"2026-05-18T03:34:00.666774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.666774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$(3,1)^*$-choosability of planar graphs without adjacent short cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andre Raspaud, Min Chen","submitted_at":"2013-02-11T20:15:58Z","abstract_excerpt":"A list assignment of a graph $G$ is a function $L$ that assigns a list $L(v)$ of colors to each vertex $v\\in V(G)$. An $(L,d)^*$-coloring is a mapping $\\pi$ that assigns a color $\\pi(v)\\in L(v)$ to each vertex $v\\in V(G)$ so that at most $d$ neighbors of $v$ receive color $\\pi(v)$. A graph $G$ is said to be $(k,d)^*$-choosable if it admits an $(L,d)^*$-coloring for every list assignment $L$ with $|L(v)|\\ge k$ for all $v\\in V(G)$. In 2001, Lih et al. \\cite{LSWZ-01} proved that planar graphs without 4- and $l$-cycles are $(3,1)^*$-choosable, where $l\\in \\{5,6,7\\}$. Later, Dong and Xu \\cite{DX-09"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2599","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":"1302.2599","created_at":"2026-05-18T03:34:00.666901+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.2599v1","created_at":"2026-05-18T03:34:00.666901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2599","created_at":"2026-05-18T03:34:00.666901+00:00"},{"alias_kind":"pith_short_12","alias_value":"JNGSZNBPCH6H","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JNGSZNBPCH6H56BF","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JNGSZNBP","created_at":"2026-05-18T12:27:49.015174+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/JNGSZNBPCH6H56BFTTCXXVABGD","json":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD.json","graph_json":"https://pith.science/api/pith-number/JNGSZNBPCH6H56BFTTCXXVABGD/graph.json","events_json":"https://pith.science/api/pith-number/JNGSZNBPCH6H56BFTTCXXVABGD/events.json","paper":"https://pith.science/paper/JNGSZNBP"},"agent_actions":{"view_html":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD","download_json":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD.json","view_paper":"https://pith.science/paper/JNGSZNBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.2599&json=true","fetch_graph":"https://pith.science/api/pith-number/JNGSZNBPCH6H56BFTTCXXVABGD/graph.json","fetch_events":"https://pith.science/api/pith-number/JNGSZNBPCH6H56BFTTCXXVABGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD/action/storage_attestation","attest_author":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD/action/author_attestation","sign_citation":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD/action/citation_signature","submit_replication":"https://pith.science/pith/JNGSZNBPCH6H56BFTTCXXVABGD/action/replication_record"}},"created_at":"2026-05-18T03:34:00.666901+00:00","updated_at":"2026-05-18T03:34:00.666901+00:00"}