{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GCIM6JSCAZKD2CHVRPBOLP6C5U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5a50d8ca31c30acf8526a548147e5a4254888a8a6255603533fc9f22d6743f0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-13T00:14:51Z","title_canon_sha256":"245e2fd228d513d7b52d95e799addafd9c33c726d1fca271ba47fbd882056eca"},"schema_version":"1.0","source":{"id":"1505.03197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03197","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03197v1","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03197","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"GCIM6JSCAZKD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GCIM6JSCAZKD2CHV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GCIM6JSC","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:2af15070ea214f0a22c2e274ad0f721f050bbcf851e0ab1cd1af0bbc0e24aab6","target":"graph","created_at":"2026-05-18T00:42:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $G$ be a planar graph without 4-cycles and 5-cycles and with maximum degree $\\Delta\\ge 32$. We prove that $\\chi_{\\ell}(G^2)\\le \\Delta+3$. For arbitrarily large maximum degree $\\Delta$, there exist planar graphs $G_{\\Delta}$ of girth 6 with $\\chi(G_{\\Delta}^2)=\\Delta+2$. Thus, our bound is within 1 of being optimal. Further, our bound comes from coloring greedily in a good order, so the bound immediately extends to online list-coloring. In addition, we prove bounds for $L(p,q)$-labeling. Specifically, $\\lambda_{2,1}(G)\\le \\Delta+8$ and, more generally, $\\lambda_{p,q}(G)\\le (2q-1)\\Delta+6p-2","authors_text":"Bobby Jaeger, Daniel W. Cranston","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-13T00:14:51Z","title":"List-coloring the Squares of Planar Graphs without 4-Cycles and 5-Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03197","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c72551e42818a38592967bf585122708940af1117289bd17725adbd0e25707f9","target":"record","created_at":"2026-05-18T00:42:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5a50d8ca31c30acf8526a548147e5a4254888a8a6255603533fc9f22d6743f0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-13T00:14:51Z","title_canon_sha256":"245e2fd228d513d7b52d95e799addafd9c33c726d1fca271ba47fbd882056eca"},"schema_version":"1.0","source":{"id":"1505.03197","kind":"arxiv","version":1}},"canonical_sha256":"3090cf264206543d08f58bc2e5bfc2ed17c2bdbf6f07258855fa27a5e730b622","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3090cf264206543d08f58bc2e5bfc2ed17c2bdbf6f07258855fa27a5e730b622","first_computed_at":"2026-05-18T00:42:33.480544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:33.480544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l20p9KDhyUDLKIJMQtAjNHVOjBZi+exE4icQ4pd4Fp3/LbuXS3lEbJzv+EhQrKWByGgLjyiheF7Ar1qD6HlRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:33.481097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c72551e42818a38592967bf585122708940af1117289bd17725adbd0e25707f9","sha256:2af15070ea214f0a22c2e274ad0f721f050bbcf851e0ab1cd1af0bbc0e24aab6"],"state_sha256":"076307f437462b07905d5b63b8899ca28ac2fa99eb1ac665aa3818030bb506bd"}