{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XP6IGZSWDFSBUC6UAH3QMBIGXT","short_pith_number":"pith:XP6IGZSW","schema_version":"1.0","canonical_sha256":"bbfc83665619641a0bd401f7060506bce12c6c1fd78e3c256474363fa3b486d7","source":{"kind":"arxiv","id":"1504.02306","version":2},"attestation_state":"computed","paper":{"title":"Optimal induced universal graphs and adjacency labeling for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mathias B{\\ae}k Tejs Knudsen, S{\\o}ren Dahlgaard, Stephen Alstrup","submitted_at":"2015-04-09T13:34:53Z","abstract_excerpt":"We show that there exists a graph $G$ with $O(n)$ nodes, where any forest of $n$ nodes is a node-induced subgraph of $G$. Furthermore, for constant arboricity $k$, the result implies the existence of a graph with $O(n^k)$ nodes that contains all $n$-node graphs as node-induced subgraphs, matching a $\\Omega(n^k)$ lower bound. The lower bound and previously best upper bounds were presented in Alstrup and Rauhe (FOCS'02). Our upper bounds are obtained through a $\\log_2 n +O(1)$ labeling scheme for adjacency queries in forests.\n  We hereby solve an open problem being raised repeatedly over decades"},"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":"1504.02306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-09T13:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"66731523672f19517ba7f6991c1db580fd858e5d90dbe53388249d5f5e7597c4","abstract_canon_sha256":"0c0e6ecfd634270bc34fe7bc498ac12ce22829a9690fa1c0767ef3c5dd085f0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:46.649609Z","signature_b64":"UWoVc4ZKaCxomixeyckR2d6tQrEWfnMSpX1f7hkumHSTqHnm4Xz8e/7P0w/gKFQaPwhEJdfm3oOFE5VBY04rAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbfc83665619641a0bd401f7060506bce12c6c1fd78e3c256474363fa3b486d7","last_reissued_at":"2026-05-18T01:20:46.649165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:46.649165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal induced universal graphs and adjacency labeling for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mathias B{\\ae}k Tejs Knudsen, S{\\o}ren Dahlgaard, Stephen Alstrup","submitted_at":"2015-04-09T13:34:53Z","abstract_excerpt":"We show that there exists a graph $G$ with $O(n)$ nodes, where any forest of $n$ nodes is a node-induced subgraph of $G$. Furthermore, for constant arboricity $k$, the result implies the existence of a graph with $O(n^k)$ nodes that contains all $n$-node graphs as node-induced subgraphs, matching a $\\Omega(n^k)$ lower bound. The lower bound and previously best upper bounds were presented in Alstrup and Rauhe (FOCS'02). Our upper bounds are obtained through a $\\log_2 n +O(1)$ labeling scheme for adjacency queries in forests.\n  We hereby solve an open problem being raised repeatedly over decades"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02306","kind":"arxiv","version":2},"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":"1504.02306","created_at":"2026-05-18T01:20:46.649233+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02306v2","created_at":"2026-05-18T01:20:46.649233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02306","created_at":"2026-05-18T01:20:46.649233+00:00"},{"alias_kind":"pith_short_12","alias_value":"XP6IGZSWDFSB","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XP6IGZSWDFSBUC6U","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XP6IGZSW","created_at":"2026-05-18T12:29:50.041715+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/XP6IGZSWDFSBUC6UAH3QMBIGXT","json":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT.json","graph_json":"https://pith.science/api/pith-number/XP6IGZSWDFSBUC6UAH3QMBIGXT/graph.json","events_json":"https://pith.science/api/pith-number/XP6IGZSWDFSBUC6UAH3QMBIGXT/events.json","paper":"https://pith.science/paper/XP6IGZSW"},"agent_actions":{"view_html":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT","download_json":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT.json","view_paper":"https://pith.science/paper/XP6IGZSW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02306&json=true","fetch_graph":"https://pith.science/api/pith-number/XP6IGZSWDFSBUC6UAH3QMBIGXT/graph.json","fetch_events":"https://pith.science/api/pith-number/XP6IGZSWDFSBUC6UAH3QMBIGXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT/action/storage_attestation","attest_author":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT/action/author_attestation","sign_citation":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT/action/citation_signature","submit_replication":"https://pith.science/pith/XP6IGZSWDFSBUC6UAH3QMBIGXT/action/replication_record"}},"created_at":"2026-05-18T01:20:46.649233+00:00","updated_at":"2026-05-18T01:20:46.649233+00:00"}