{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AQRJ5SAUAXVFMVS3OCH6XRGKH3","short_pith_number":"pith:AQRJ5SAU","schema_version":"1.0","canonical_sha256":"04229ec81405ea56565b708febc4ca3eea853f1dece40e4138084ed307789347","source":{"kind":"arxiv","id":"1504.03670","version":3},"attestation_state":"computed","paper":{"title":"Coloring Graphs having Few Colorings over Path Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andreas Bj\\\"orklund","submitted_at":"2015-04-14T19:44:39Z","abstract_excerpt":"Lokshtanov, Marx, and Saurabh SODA 2011 proved that there is no $(k-\\epsilon)^{\\operatorname{pw}(G)}\\operatorname{poly}(n)$ time algorithm for deciding if an $n$-vertex graph $G$ with pathwidth $\\operatorname{pw}(G)$ admits a proper vertex coloring with $k$ colors unless the Strong Exponential Time Hypothesis (SETH) is false. We show here that nevertheless, when $k>\\lfloor \\Delta/2 \\rfloor + 1$, where $\\Delta$ is the maximum degree in the graph $G$, there is a better algorithm, at least when there are few colorings. We present a Monte Carlo algorithm that given a graph $G$ along with a path de"},"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":"1504.03670","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-14T19:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"7370abbc29599ed522a9d68aecc48cd4434a35f4c43cb713d795d69d89214c90","abstract_canon_sha256":"f1e1cfb04ed41587c718e3ab9c58d07fe2d4f7ef2d25a1cb50b8ef6fbf305aed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:07.382397Z","signature_b64":"D8dV7NhOTvffIBItbz7syT9gH4uvp6kgVykuRyq4r3pqXMLtqGjHGfPZlXxPPL8P+oXN+fp6ZPyViVABFsrcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04229ec81405ea56565b708febc4ca3eea853f1dece40e4138084ed307789347","last_reissued_at":"2026-05-18T01:37:07.381946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:07.381946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring Graphs having Few Colorings over Path Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andreas Bj\\\"orklund","submitted_at":"2015-04-14T19:44:39Z","abstract_excerpt":"Lokshtanov, Marx, and Saurabh SODA 2011 proved that there is no $(k-\\epsilon)^{\\operatorname{pw}(G)}\\operatorname{poly}(n)$ time algorithm for deciding if an $n$-vertex graph $G$ with pathwidth $\\operatorname{pw}(G)$ admits a proper vertex coloring with $k$ colors unless the Strong Exponential Time Hypothesis (SETH) is false. We show here that nevertheless, when $k>\\lfloor \\Delta/2 \\rfloor + 1$, where $\\Delta$ is the maximum degree in the graph $G$, there is a better algorithm, at least when there are few colorings. We present a Monte Carlo algorithm that given a graph $G$ along with a path de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03670","kind":"arxiv","version":3},"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":"1504.03670","created_at":"2026-05-18T01:37:07.382013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03670v3","created_at":"2026-05-18T01:37:07.382013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03670","created_at":"2026-05-18T01:37:07.382013+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQRJ5SAUAXVF","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQRJ5SAUAXVFMVS3","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQRJ5SAU","created_at":"2026-05-18T12:29:10.953037+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/AQRJ5SAUAXVFMVS3OCH6XRGKH3","json":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3.json","graph_json":"https://pith.science/api/pith-number/AQRJ5SAUAXVFMVS3OCH6XRGKH3/graph.json","events_json":"https://pith.science/api/pith-number/AQRJ5SAUAXVFMVS3OCH6XRGKH3/events.json","paper":"https://pith.science/paper/AQRJ5SAU"},"agent_actions":{"view_html":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3","download_json":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3.json","view_paper":"https://pith.science/paper/AQRJ5SAU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03670&json=true","fetch_graph":"https://pith.science/api/pith-number/AQRJ5SAUAXVFMVS3OCH6XRGKH3/graph.json","fetch_events":"https://pith.science/api/pith-number/AQRJ5SAUAXVFMVS3OCH6XRGKH3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3/action/storage_attestation","attest_author":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3/action/author_attestation","sign_citation":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3/action/citation_signature","submit_replication":"https://pith.science/pith/AQRJ5SAUAXVFMVS3OCH6XRGKH3/action/replication_record"}},"created_at":"2026-05-18T01:37:07.382013+00:00","updated_at":"2026-05-18T01:37:07.382013+00:00"}