{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IBWWZYLK2IZARDETZDCVSQOBAT","short_pith_number":"pith:IBWWZYLK","schema_version":"1.0","canonical_sha256":"406d6ce16ad232088c93c8c55941c104c0a472cb23ef180d3767305863b64fc1","source":{"kind":"arxiv","id":"1608.06142","version":2},"attestation_state":"computed","paper":{"title":"Squares of Low Maximum Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Anthony Stewart, Dani\\\"el Paulusma, Dieter Kratsch, Jean-Fran\\c{c}ois Couturier, Manfred Cochefert, Petr A. Golovach","submitted_at":"2016-08-22T12:18:30Z","abstract_excerpt":"A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed graph classes and a very limited number of other graph classes. We prove that Square Root is O(n)-time solvable for graphs of maximum degree 5 and O(n^4)-time solvable for graphs of maximum degree at most 6."},"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":"1608.06142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-08-22T12:18:30Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"be497966874b87a7a183ed7fe7bcbc7ca04a71148123bdaa11921a5bb4c96d0f","abstract_canon_sha256":"d10e5f55f09515a5675d46f44544a75c51d5457fe1553134863e5e68c09c21f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:50.432359Z","signature_b64":"1IMJ3hVCuDuRxDYa/tGhAKxdPMKZVzTHbiyuVHj15t3R7UJh54+XRAPUlxBWB6z5EeG3bhdKQoKjksG5QU5SCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"406d6ce16ad232088c93c8c55941c104c0a472cb23ef180d3767305863b64fc1","last_reissued_at":"2026-05-18T01:07:50.431826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:50.431826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Squares of Low Maximum Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Anthony Stewart, Dani\\\"el Paulusma, Dieter Kratsch, Jean-Fran\\c{c}ois Couturier, Manfred Cochefert, Petr A. Golovach","submitted_at":"2016-08-22T12:18:30Z","abstract_excerpt":"A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed graph classes and a very limited number of other graph classes. We prove that Square Root is O(n)-time solvable for graphs of maximum degree 5 and O(n^4)-time solvable for graphs of maximum degree at most 6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06142","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":"1608.06142","created_at":"2026-05-18T01:07:50.431914+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.06142v2","created_at":"2026-05-18T01:07:50.431914+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06142","created_at":"2026-05-18T01:07:50.431914+00:00"},{"alias_kind":"pith_short_12","alias_value":"IBWWZYLK2IZA","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IBWWZYLK2IZARDET","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IBWWZYLK","created_at":"2026-05-18T12:30:22.444734+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/IBWWZYLK2IZARDETZDCVSQOBAT","json":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT.json","graph_json":"https://pith.science/api/pith-number/IBWWZYLK2IZARDETZDCVSQOBAT/graph.json","events_json":"https://pith.science/api/pith-number/IBWWZYLK2IZARDETZDCVSQOBAT/events.json","paper":"https://pith.science/paper/IBWWZYLK"},"agent_actions":{"view_html":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT","download_json":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT.json","view_paper":"https://pith.science/paper/IBWWZYLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.06142&json=true","fetch_graph":"https://pith.science/api/pith-number/IBWWZYLK2IZARDETZDCVSQOBAT/graph.json","fetch_events":"https://pith.science/api/pith-number/IBWWZYLK2IZARDETZDCVSQOBAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT/action/storage_attestation","attest_author":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT/action/author_attestation","sign_citation":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT/action/citation_signature","submit_replication":"https://pith.science/pith/IBWWZYLK2IZARDETZDCVSQOBAT/action/replication_record"}},"created_at":"2026-05-18T01:07:50.431914+00:00","updated_at":"2026-05-18T01:07:50.431914+00:00"}