{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MISRNCPHJBKYIH5HXINY3DLKPI","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":"2314fa55ee5a1a97668cb647a26efe8360101d464356dade89cbcd16da1fc3ae","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-09T15:22:35Z","title_canon_sha256":"fc2d9105d123085b485094ba14eadbe3b36c316fb635d2d8e758e7eaf8cd93fd"},"schema_version":"1.0","source":{"id":"1811.03966","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03966","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03966v2","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03966","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"MISRNCPHJBKY","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MISRNCPHJBKYIH5H","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MISRNCPH","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:345a5f7fc1c44db8b02ff76f04342484505b64d5dd167f98fdac86b688453285","target":"graph","created_at":"2026-05-17T23:54:22Z","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":"A $b$-coloring of a graph $G$ is a proper coloring of its vertices such that each color class contains a vertex that has at least one neighbor in all the other color classes. The b-Coloring problem asks whether a graph $G$ has a $b$-coloring with $k$ colors. The $b$-chromatic number of a graph $G$, denoted by $\\chi_b(G)$, is the maximum number $k$ such that $G$ admits a $b$-coloring with $k$ colors. We consider the complexity of the b-Coloring problem, whenever the value of $k$ is close to one of two upper bounds on $\\chi_b(G)$: The maximum degree $\\Delta(G)$ plus one, and the $m$-degree, deno","authors_text":"Lars Jaffke, Paloma T. Lima","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-09T15:22:35Z","title":"A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03966","kind":"arxiv","version":2},"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:a23dd3175c210a075814515029121247fcff8a1bc9ae24da4a89c8b7d6abf742","target":"record","created_at":"2026-05-17T23:54:22Z","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":"2314fa55ee5a1a97668cb647a26efe8360101d464356dade89cbcd16da1fc3ae","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-09T15:22:35Z","title_canon_sha256":"fc2d9105d123085b485094ba14eadbe3b36c316fb635d2d8e758e7eaf8cd93fd"},"schema_version":"1.0","source":{"id":"1811.03966","kind":"arxiv","version":2}},"canonical_sha256":"62251689e74855841fa7ba1b8d8d6a7a3887a6671b7c560bef8881d554bc3bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62251689e74855841fa7ba1b8d8d6a7a3887a6671b7c560bef8881d554bc3bef","first_computed_at":"2026-05-17T23:54:22.100988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:22.100988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rvDxnLQ7JXU80gOayk5uEXFDni+vfo7bYb3SPbOFig0qSNfST0fNyZwVhuf4FusGZ/hPRncD4rQ5+uKGm5dwDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:22.101762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03966","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a23dd3175c210a075814515029121247fcff8a1bc9ae24da4a89c8b7d6abf742","sha256:345a5f7fc1c44db8b02ff76f04342484505b64d5dd167f98fdac86b688453285"],"state_sha256":"5ca1e85c7af1d09a0122d600b40f97f53876d9efb89e800aa91b7f81ed00e374"}