{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:J2Z4OJPQ3O6MYVIXOH2RLAIM4V","short_pith_number":"pith:J2Z4OJPQ","schema_version":"1.0","canonical_sha256":"4eb3c725f0dbbccc551771f515810ce54832c1ef43211dc98a23421c4c696c53","source":{"kind":"arxiv","id":"1504.06176","version":3},"attestation_state":"computed","paper":{"title":"Properly colored and rainbow copies of graphs with few cherries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Jan Volec","submitted_at":"2015-04-23T13:39:06Z","abstract_excerpt":"Let G be an n-vertex graph that contains linearly many cherries (i.e., paths on 3 vertices), and let c be a coloring of the edges of the complete graph K_n such that at each vertex every color appears only constantly many times. In 1979, Shearer conjectured that such a coloring c must contain a properly colored copy of G. We establish this conjecture in a strong form, showing that it holds even for graphs G with O(n^(4/3)) cherries and moreover this bound on the number of cherries is best possible up to a constant factor. We also prove that one can find a rainbow copy of such G in every edge-c"},"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":"1504.06176","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-23T13:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"d74b05707e8889f3000d17a43a2d3f528fad94886c491457e3d53cb747b374d6","abstract_canon_sha256":"8bb04bddc4bb320e1947db6f1988440767c6e5fe3edbb9efcbe083b2e57f5b5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:03.530939Z","signature_b64":"LVoY/WNIMfsT7I0MqthgTAWVKkYVTFaO6W4oLg2pYCFOGnF1/Tz24tiokHNXbKHqwY1qYuSrJ2fSC+e0UGzoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eb3c725f0dbbccc551771f515810ce54832c1ef43211dc98a23421c4c696c53","last_reissued_at":"2026-05-18T01:11:03.530485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:03.530485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Properly colored and rainbow copies of graphs with few cherries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Jan Volec","submitted_at":"2015-04-23T13:39:06Z","abstract_excerpt":"Let G be an n-vertex graph that contains linearly many cherries (i.e., paths on 3 vertices), and let c be a coloring of the edges of the complete graph K_n such that at each vertex every color appears only constantly many times. In 1979, Shearer conjectured that such a coloring c must contain a properly colored copy of G. We establish this conjecture in a strong form, showing that it holds even for graphs G with O(n^(4/3)) cherries and moreover this bound on the number of cherries is best possible up to a constant factor. We also prove that one can find a rainbow copy of such G in every edge-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06176","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":"1504.06176","created_at":"2026-05-18T01:11:03.530564+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06176v3","created_at":"2026-05-18T01:11:03.530564+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06176","created_at":"2026-05-18T01:11:03.530564+00:00"},{"alias_kind":"pith_short_12","alias_value":"J2Z4OJPQ3O6M","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"J2Z4OJPQ3O6MYVIX","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"J2Z4OJPQ","created_at":"2026-05-18T12:29:27.538025+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/J2Z4OJPQ3O6MYVIXOH2RLAIM4V","json":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V.json","graph_json":"https://pith.science/api/pith-number/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/graph.json","events_json":"https://pith.science/api/pith-number/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/events.json","paper":"https://pith.science/paper/J2Z4OJPQ"},"agent_actions":{"view_html":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V","download_json":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V.json","view_paper":"https://pith.science/paper/J2Z4OJPQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06176&json=true","fetch_graph":"https://pith.science/api/pith-number/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/graph.json","fetch_events":"https://pith.science/api/pith-number/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/action/storage_attestation","attest_author":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/action/author_attestation","sign_citation":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/action/citation_signature","submit_replication":"https://pith.science/pith/J2Z4OJPQ3O6MYVIXOH2RLAIM4V/action/replication_record"}},"created_at":"2026-05-18T01:11:03.530564+00:00","updated_at":"2026-05-18T01:11:03.530564+00:00"}