{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LNBNPUYMRG6S6ZIVUE6ZDYPRFX","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":"881fb43ffc889f886a9da4c6c9ad1ea74b118021cdc22ab27d7da65ccdbb3f8e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-24T17:13:26Z","title_canon_sha256":"02ec2f8865eccff5d8d23df28682932960ec46adb6e7c69a4bf9bf30a32ecfdb"},"schema_version":"1.0","source":{"id":"1701.06985","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06985","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06985v1","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06985","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"LNBNPUYMRG6S","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LNBNPUYMRG6S6ZIV","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LNBNPUYM","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:60e3a24c307ba58d092281f68d15a08cf257a9f70b63f7f1097ed749160b0c5d","target":"graph","created_at":"2026-05-18T00:52:09Z","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":"The $q$-Coloring problem asks whether the vertices of a graph can be properly colored with $q$ colors. Lokshtanov et al. [SODA 2011] showed that $q$-Coloring on graphs with a feedback vertex set of size $k$ cannot be solved in time $\\mathcal{O}^*((q-\\varepsilon)^k)$, for any $\\varepsilon > 0$, unless the Strong Exponential-Time Hypothesis (SETH) fails. In this paper we perform a fine-grained analysis of the complexity of $q$-Coloring with respect to a hierarchy of parameters. We show that even when parameterized by the vertex cover number, $q$ must appear in the base of the exponent: Unless ET","authors_text":"Bart M. P. Jansen, Lars Jaffke","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-24T17:13:26Z","title":"Fine-Grained Parameterized Complexity Analysis of Graph Coloring Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06985","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":"sha256:827d28ef9911fd60bf304643583feb9fbfc63edf011f23f6976937ef4e0c38ea","target":"record","created_at":"2026-05-18T00:52:09Z","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":"881fb43ffc889f886a9da4c6c9ad1ea74b118021cdc22ab27d7da65ccdbb3f8e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-24T17:13:26Z","title_canon_sha256":"02ec2f8865eccff5d8d23df28682932960ec46adb6e7c69a4bf9bf30a32ecfdb"},"schema_version":"1.0","source":{"id":"1701.06985","kind":"arxiv","version":1}},"canonical_sha256":"5b42d7d30c89bd2f6515a13d91e1f12dda62115ed0ccbbf51dee34470c2c8ff9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b42d7d30c89bd2f6515a13d91e1f12dda62115ed0ccbbf51dee34470c2c8ff9","first_computed_at":"2026-05-18T00:52:09.974108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:09.974108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P8zd4G64cg1HF1MKyxnj8aRqI+xTcY5ENU2S71iBiQ8WIF4dzIoyt97vezVmEa/iDN1r3HfqHXt9atAugY/5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:09.974731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06985","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:827d28ef9911fd60bf304643583feb9fbfc63edf011f23f6976937ef4e0c38ea","sha256:60e3a24c307ba58d092281f68d15a08cf257a9f70b63f7f1097ed749160b0c5d"],"state_sha256":"cf56ec4a714e194b3dd6c9327c850e6e8850d293a3aba1487e939f16ea1122c7"}