{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7FHJRNVJC634B2YDNGFHTE6X4K","short_pith_number":"pith:7FHJRNVJ","schema_version":"1.0","canonical_sha256":"f94e98b6a917b7c0eb03698a7993d7e2aa346a51c840f5c6c66b39b47f961cc8","source":{"kind":"arxiv","id":"1904.07728","version":2},"attestation_state":"computed","paper":{"title":"On restricted colorings of $(d,s)$-edge colorable graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lan Anh Pham","submitted_at":"2019-04-15T14:22:26Z","abstract_excerpt":"A cycle is $2$-colored if its edges are properly colored by two distinct colors. A $(d,s)$-edge colorable graph $G$ is a $d$-regular graph that admits a proper $d$-edge coloring in which every edge of $G$ is in at least $s-1$ $2$-colored $4$-cycles. Given a $(d,s)$-edge colorable graph $G$ and a list assigment $L$ of forbidden colors for the edges of $G$ satisfying certain sparsity conditions, we prove that there is a proper $d$-edge coloring of $G$ that avoids $L$, that is, a proper edge coloring $\\varphi$ of $G$ such that $\\varphi(e) \\notin L(e)$ for every edge $e$ of $G$."},"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":"1904.07728","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-04-15T14:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"6025abd4b08d1dd1ed8a0171b092573a6d17321060fd9f8129d081d50e300f45","abstract_canon_sha256":"fd6be491c7b80f6bfa27aeaac849fab805e5b746f7f43dbe581493da2aac3d50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:08.977750Z","signature_b64":"FWuT2FKN7pzMnkCgy+bWXTiX9zwvpwYs/8WrhV8pJYe0giatO3qd+hmYX9qOB1q5Rnn9luEC6luuVP0fti5CAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f94e98b6a917b7c0eb03698a7993d7e2aa346a51c840f5c6c66b39b47f961cc8","last_reissued_at":"2026-05-17T23:45:08.977091Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:08.977091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On restricted colorings of $(d,s)$-edge colorable graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lan Anh Pham","submitted_at":"2019-04-15T14:22:26Z","abstract_excerpt":"A cycle is $2$-colored if its edges are properly colored by two distinct colors. A $(d,s)$-edge colorable graph $G$ is a $d$-regular graph that admits a proper $d$-edge coloring in which every edge of $G$ is in at least $s-1$ $2$-colored $4$-cycles. Given a $(d,s)$-edge colorable graph $G$ and a list assigment $L$ of forbidden colors for the edges of $G$ satisfying certain sparsity conditions, we prove that there is a proper $d$-edge coloring of $G$ that avoids $L$, that is, a proper edge coloring $\\varphi$ of $G$ such that $\\varphi(e) \\notin L(e)$ for every edge $e$ of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07728","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":"1904.07728","created_at":"2026-05-17T23:45:08.977194+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07728v2","created_at":"2026-05-17T23:45:08.977194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07728","created_at":"2026-05-17T23:45:08.977194+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FHJRNVJC634","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FHJRNVJC634B2YD","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FHJRNVJ","created_at":"2026-05-18T12:33:12.712433+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/7FHJRNVJC634B2YDNGFHTE6X4K","json":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K.json","graph_json":"https://pith.science/api/pith-number/7FHJRNVJC634B2YDNGFHTE6X4K/graph.json","events_json":"https://pith.science/api/pith-number/7FHJRNVJC634B2YDNGFHTE6X4K/events.json","paper":"https://pith.science/paper/7FHJRNVJ"},"agent_actions":{"view_html":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K","download_json":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K.json","view_paper":"https://pith.science/paper/7FHJRNVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07728&json=true","fetch_graph":"https://pith.science/api/pith-number/7FHJRNVJC634B2YDNGFHTE6X4K/graph.json","fetch_events":"https://pith.science/api/pith-number/7FHJRNVJC634B2YDNGFHTE6X4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K/action/storage_attestation","attest_author":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K/action/author_attestation","sign_citation":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K/action/citation_signature","submit_replication":"https://pith.science/pith/7FHJRNVJC634B2YDNGFHTE6X4K/action/replication_record"}},"created_at":"2026-05-17T23:45:08.977194+00:00","updated_at":"2026-05-17T23:45:08.977194+00:00"}