{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UTCDNEIDEOCP3UKTMRUSASTDZK","short_pith_number":"pith:UTCDNEID","schema_version":"1.0","canonical_sha256":"a4c43691032384fdd1536469204a63cab918d0ef301d82f05319ed079879019b","source":{"kind":"arxiv","id":"1508.01129","version":1},"attestation_state":"computed","paper":{"title":"On decomposing graphs of large minimum degree into locally irregular subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jakub Przyby{\\l}o","submitted_at":"2015-08-05T17:02:05Z","abstract_excerpt":"A \\emph{locally irregular graph} is a graph whose adjacent vertices have distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally irregular subgraphs if its edge set may be partitioned into $k$ subsets each of which induces a locally irregular subgraph in $G$. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles and a special class of graphs of maximum degree $3$, every connected graph can be decomposed into $3$ locally irregular subgraphs. Using a combination of a probabilistic approach and some kn"},"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":"1508.01129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-05T17:02:05Z","cross_cats_sorted":[],"title_canon_sha256":"3868bba4d162c071e70df7bd4b6df9a6ac0b1462c6060faa458fdd3dd0d2d9ed","abstract_canon_sha256":"2d4c461ce4a6544aab3c5ae24718ed2fcacd41d2c61884e0783a3dcc26ef2315"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:47.287925Z","signature_b64":"zqlZ/46COgh4s3HDTQvgXXmGMPOovsTBz8zGRm+XWnQ/LJmdDFzJfcpksv+RKBSd5m6xZZnXUDq+w05eFVpIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4c43691032384fdd1536469204a63cab918d0ef301d82f05319ed079879019b","last_reissued_at":"2026-05-18T00:49:47.287289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:47.287289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On decomposing graphs of large minimum degree into locally irregular subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jakub Przyby{\\l}o","submitted_at":"2015-08-05T17:02:05Z","abstract_excerpt":"A \\emph{locally irregular graph} is a graph whose adjacent vertices have distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally irregular subgraphs if its edge set may be partitioned into $k$ subsets each of which induces a locally irregular subgraph in $G$. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles and a special class of graphs of maximum degree $3$, every connected graph can be decomposed into $3$ locally irregular subgraphs. Using a combination of a probabilistic approach and some kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01129","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":"1508.01129","created_at":"2026-05-18T00:49:47.287417+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01129v1","created_at":"2026-05-18T00:49:47.287417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01129","created_at":"2026-05-18T00:49:47.287417+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTCDNEIDEOCP","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTCDNEIDEOCP3UKT","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTCDNEID","created_at":"2026-05-18T12:29:44.643036+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/UTCDNEIDEOCP3UKTMRUSASTDZK","json":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK.json","graph_json":"https://pith.science/api/pith-number/UTCDNEIDEOCP3UKTMRUSASTDZK/graph.json","events_json":"https://pith.science/api/pith-number/UTCDNEIDEOCP3UKTMRUSASTDZK/events.json","paper":"https://pith.science/paper/UTCDNEID"},"agent_actions":{"view_html":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK","download_json":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK.json","view_paper":"https://pith.science/paper/UTCDNEID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01129&json=true","fetch_graph":"https://pith.science/api/pith-number/UTCDNEIDEOCP3UKTMRUSASTDZK/graph.json","fetch_events":"https://pith.science/api/pith-number/UTCDNEIDEOCP3UKTMRUSASTDZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK/action/storage_attestation","attest_author":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK/action/author_attestation","sign_citation":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK/action/citation_signature","submit_replication":"https://pith.science/pith/UTCDNEIDEOCP3UKTMRUSASTDZK/action/replication_record"}},"created_at":"2026-05-18T00:49:47.287417+00:00","updated_at":"2026-05-18T00:49:47.287417+00:00"}