{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O5X25HAEDLIWRAUL6ZCUIPHYOH","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":"6287965df7856e1802df804467f16442115bd3005e6194c54fe80292817445d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T21:55:20Z","title_canon_sha256":"742f98ca5f472c3773bacd935c13cb13ef4e0052c309c123dc56c0321c7c3a0c"},"schema_version":"1.0","source":{"id":"1505.06234","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06234","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06234v3","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06234","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"O5X25HAEDLIW","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O5X25HAEDLIWRAUL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O5X25HAE","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:8ab9011558668b835b014caca0d008b1d68266875cbfe8eb695c665f6c443e29","target":"graph","created_at":"2026-05-18T00:54:15Z","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":"For a graph $G$ and a tree-decomposition $(T, \\mathcal{B})$ of $G$, the chromatic number of $(T, \\mathcal{B})$ is the maximum of $\\chi(G[B])$, taken over all bags $B \\in \\mathcal{B}$. The tree-chromatic number of $G$ is the minimum chromatic number of all tree-decompositions $(T, \\mathcal{B})$ of $G$. The path-chromatic number of $G$ is defined analogously. In this paper, we introduce an operation that always increases the path-chromatic number of a graph. As an easy corollary of our construction, we obtain an infinite family of graphs whose path-chromatic number and tree-chromatic number are ","authors_text":"Ringi Kim, Tony Huynh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T21:55:20Z","title":"Tree-chromatic number is not equal to path-chromatic number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06234","kind":"arxiv","version":3},"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:e19d85d5ad4d01efedcdc9e264ef1db941463ca27e3e61f375212f919ec19df7","target":"record","created_at":"2026-05-18T00:54:15Z","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":"6287965df7856e1802df804467f16442115bd3005e6194c54fe80292817445d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T21:55:20Z","title_canon_sha256":"742f98ca5f472c3773bacd935c13cb13ef4e0052c309c123dc56c0321c7c3a0c"},"schema_version":"1.0","source":{"id":"1505.06234","kind":"arxiv","version":3}},"canonical_sha256":"776fae9c041ad168828bf645443cf871dcf6d07000baf601d859f61867078f57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"776fae9c041ad168828bf645443cf871dcf6d07000baf601d859f61867078f57","first_computed_at":"2026-05-18T00:54:15.909016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.909016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s6gkzC2jkBfqH/AqtFIWPL8qfg1s1Bz+LT8V9qNvCkZhgX9d50UsVQxNXrk5M/zLl2K9OuB3G15w/Y72hWSSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.909473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06234","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e19d85d5ad4d01efedcdc9e264ef1db941463ca27e3e61f375212f919ec19df7","sha256:8ab9011558668b835b014caca0d008b1d68266875cbfe8eb695c665f6c443e29"],"state_sha256":"db0d5d6a5c93b9cd332c8a16da62483a4156af65ab7f32bca956da299c24aedc"}