{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ETMKDTLF4CZKKREYFUPUXMAAQW","short_pith_number":"pith:ETMKDTLF","schema_version":"1.0","canonical_sha256":"24d8a1cd65e0b2a544982d1f4bb00085aad868adc80f1c714cf6d56df27d8a68","source":{"kind":"arxiv","id":"1602.05608","version":1},"attestation_state":"computed","paper":{"title":"On the fine-grained complexity of rainbow coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Arkadiusz Soca{\\l}a, Juho Lauri, {\\L}ukasz Kowalik","submitted_at":"2016-02-17T21:49:16Z","abstract_excerpt":"The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in $k$ colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any $k\\ge 2$, there is no algorithm for Rainbow k-Coloring running in time $2^{o(n^{3/2})}$, unless ETH fails.\n  Motivated by this negative result we consider two parameterized variants of the problem. In Subset Rainbow k-Coloring problem, introduced by Chakraborty et al. [STACS 2009, J. Comb. Opt. 2009], we are additionally given a set $S$ of pairs of v"},"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":"1602.05608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-17T21:49:16Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"666e54d80bdc024e47447db5a6aecc71d251a3dd38dc3126191b0813fb450306","abstract_canon_sha256":"c1b72fa2e0299b9973343662b23028d1f0805aa635795f0d02a6be86898f52fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.680853Z","signature_b64":"BptvFav06YbjyjoGDolAuvBHyVavP98MKSV8xtv/QdV8+1J6fy50z1btpRoRAdEgWhIyL0bxARxUM2rxUlS2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24d8a1cd65e0b2a544982d1f4bb00085aad868adc80f1c714cf6d56df27d8a68","last_reissued_at":"2026-05-18T01:20:23.680248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.680248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the fine-grained complexity of rainbow coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Arkadiusz Soca{\\l}a, Juho Lauri, {\\L}ukasz Kowalik","submitted_at":"2016-02-17T21:49:16Z","abstract_excerpt":"The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in $k$ colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any $k\\ge 2$, there is no algorithm for Rainbow k-Coloring running in time $2^{o(n^{3/2})}$, unless ETH fails.\n  Motivated by this negative result we consider two parameterized variants of the problem. In Subset Rainbow k-Coloring problem, introduced by Chakraborty et al. [STACS 2009, J. Comb. Opt. 2009], we are additionally given a set $S$ of pairs of v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05608","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":"1602.05608","created_at":"2026-05-18T01:20:23.680357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05608v1","created_at":"2026-05-18T01:20:23.680357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05608","created_at":"2026-05-18T01:20:23.680357+00:00"},{"alias_kind":"pith_short_12","alias_value":"ETMKDTLF4CZK","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"ETMKDTLF4CZKKREY","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"ETMKDTLF","created_at":"2026-05-18T12:30:15.759754+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/ETMKDTLF4CZKKREYFUPUXMAAQW","json":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW.json","graph_json":"https://pith.science/api/pith-number/ETMKDTLF4CZKKREYFUPUXMAAQW/graph.json","events_json":"https://pith.science/api/pith-number/ETMKDTLF4CZKKREYFUPUXMAAQW/events.json","paper":"https://pith.science/paper/ETMKDTLF"},"agent_actions":{"view_html":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW","download_json":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW.json","view_paper":"https://pith.science/paper/ETMKDTLF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05608&json=true","fetch_graph":"https://pith.science/api/pith-number/ETMKDTLF4CZKKREYFUPUXMAAQW/graph.json","fetch_events":"https://pith.science/api/pith-number/ETMKDTLF4CZKKREYFUPUXMAAQW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW/action/storage_attestation","attest_author":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW/action/author_attestation","sign_citation":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW/action/citation_signature","submit_replication":"https://pith.science/pith/ETMKDTLF4CZKKREYFUPUXMAAQW/action/replication_record"}},"created_at":"2026-05-18T01:20:23.680357+00:00","updated_at":"2026-05-18T01:20:23.680357+00:00"}