{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PLFQAEA25NC7Y45A6E4RZSR3A7","short_pith_number":"pith:PLFQAEA2","schema_version":"1.0","canonical_sha256":"7acb00101aeb45fc73a0f1391cca3b07fb5b8432a77b59799d42cb8bf6cb544d","source":{"kind":"arxiv","id":"1502.05447","version":1},"attestation_state":"computed","paper":{"title":"Lower Bounds for the Graph Homomorphism Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexander Golovnev, Alexander S. Kulikov, Fedor V. Fomin, Ivan Mihajlin","submitted_at":"2015-02-19T00:12:26Z","abstract_excerpt":"The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\\Omega\\left( \\frac{n \\log h}{\\log \\log h}\\right)}$. This rules out the existence of a single-exponential algorithm"},"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":"1502.05447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-19T00:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"71452054792501958b3d9a33f3c5f74530eb8468d6768ca70b297956a00bd5a6","abstract_canon_sha256":"24b81cd749940bd2d13cc06d3010d46507a987e8ba6bb9f9b9f58e732bcf8dc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:46.516603Z","signature_b64":"mmjOnTlXuTu+rmiO8GZkxgkwFQjDFfuyoLQNWUObY0BMlh/p4sh2j9YduRLX7J5B2nBD1FDMjvzYzoPvzgiKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7acb00101aeb45fc73a0f1391cca3b07fb5b8432a77b59799d42cb8bf6cb544d","last_reissued_at":"2026-05-18T02:26:46.516146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:46.516146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower Bounds for the Graph Homomorphism Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexander Golovnev, Alexander S. Kulikov, Fedor V. Fomin, Ivan Mihajlin","submitted_at":"2015-02-19T00:12:26Z","abstract_excerpt":"The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\\Omega\\left( \\frac{n \\log h}{\\log \\log h}\\right)}$. This rules out the existence of a single-exponential algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05447","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":"1502.05447","created_at":"2026-05-18T02:26:46.516209+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05447v1","created_at":"2026-05-18T02:26:46.516209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05447","created_at":"2026-05-18T02:26:46.516209+00:00"},{"alias_kind":"pith_short_12","alias_value":"PLFQAEA25NC7","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PLFQAEA25NC7Y45A","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PLFQAEA2","created_at":"2026-05-18T12:29:37.295048+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/PLFQAEA25NC7Y45A6E4RZSR3A7","json":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7.json","graph_json":"https://pith.science/api/pith-number/PLFQAEA25NC7Y45A6E4RZSR3A7/graph.json","events_json":"https://pith.science/api/pith-number/PLFQAEA25NC7Y45A6E4RZSR3A7/events.json","paper":"https://pith.science/paper/PLFQAEA2"},"agent_actions":{"view_html":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7","download_json":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7.json","view_paper":"https://pith.science/paper/PLFQAEA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05447&json=true","fetch_graph":"https://pith.science/api/pith-number/PLFQAEA25NC7Y45A6E4RZSR3A7/graph.json","fetch_events":"https://pith.science/api/pith-number/PLFQAEA25NC7Y45A6E4RZSR3A7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7/action/storage_attestation","attest_author":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7/action/author_attestation","sign_citation":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7/action/citation_signature","submit_replication":"https://pith.science/pith/PLFQAEA25NC7Y45A6E4RZSR3A7/action/replication_record"}},"created_at":"2026-05-18T02:26:46.516209+00:00","updated_at":"2026-05-18T02:26:46.516209+00:00"}