{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FHZLSI4Z5ET566QUEGAYWI34NE","short_pith_number":"pith:FHZLSI4Z","schema_version":"1.0","canonical_sha256":"29f2b92399e927df7a1421818b237c690ae762ef15dc39e381441de57d0464e6","source":{"kind":"arxiv","id":"1506.05719","version":2},"attestation_state":"computed","paper":{"title":"A Coloring Algorithm for $4K_1$-free line graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ang\\`ele M. Hamel, Ch\\'inh T. Ho\\`ang, Dallas J. Fraser","submitted_at":"2015-06-18T15:30:48Z","abstract_excerpt":"Let $L$ be a set of graphs. $Free$($L$) is the set of graphs that do not contain any graph in $L$ as an induced subgraph. It is known that if $L$ is a set of four-vertex graphs, then the complexity of the coloring problem for $Free$($L$) is known with three exceptions: $L $= {claw, $4K_1$}, $L$ = {claw, $4K_1$, co-diamond}, and $L$ = {$C_4$, $4K_1$}. In this paper, we study the coloring problem for $Free$(claw, $4K_1$). We solve the coloring problem for a subclass of $Free$(claw, $4K_1$) which contains the class of $4K_1$-free line graphs. Our result implies the chromatic index of a graph with"},"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":"1506.05719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-18T15:30:48Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"a0303855111264d6e376db6cec678328c336793e5ba4d8a67234fb7c93e40572","abstract_canon_sha256":"a158dc9f4ab58e0e6b477cc768aad0330cff5b22de6536f094e3662e1218479a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:51.674536Z","signature_b64":"KSlelsWbRQ3doh9Othr5iYcVCncAdID+tLRjQHoKxbswNFSCvlOiNoJUmTTeEwVLreLnl2iB9TFJiEZBjaHaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29f2b92399e927df7a1421818b237c690ae762ef15dc39e381441de57d0464e6","last_reissued_at":"2026-05-18T01:38:51.674014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:51.674014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Coloring Algorithm for $4K_1$-free line graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ang\\`ele M. Hamel, Ch\\'inh T. Ho\\`ang, Dallas J. Fraser","submitted_at":"2015-06-18T15:30:48Z","abstract_excerpt":"Let $L$ be a set of graphs. $Free$($L$) is the set of graphs that do not contain any graph in $L$ as an induced subgraph. It is known that if $L$ is a set of four-vertex graphs, then the complexity of the coloring problem for $Free$($L$) is known with three exceptions: $L $= {claw, $4K_1$}, $L$ = {claw, $4K_1$, co-diamond}, and $L$ = {$C_4$, $4K_1$}. In this paper, we study the coloring problem for $Free$(claw, $4K_1$). We solve the coloring problem for a subclass of $Free$(claw, $4K_1$) which contains the class of $4K_1$-free line graphs. Our result implies the chromatic index of a graph with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05719","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":"1506.05719","created_at":"2026-05-18T01:38:51.674089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.05719v2","created_at":"2026-05-18T01:38:51.674089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05719","created_at":"2026-05-18T01:38:51.674089+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHZLSI4Z5ET5","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHZLSI4Z5ET566QU","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHZLSI4Z","created_at":"2026-05-18T12:29:19.899920+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/FHZLSI4Z5ET566QUEGAYWI34NE","json":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE.json","graph_json":"https://pith.science/api/pith-number/FHZLSI4Z5ET566QUEGAYWI34NE/graph.json","events_json":"https://pith.science/api/pith-number/FHZLSI4Z5ET566QUEGAYWI34NE/events.json","paper":"https://pith.science/paper/FHZLSI4Z"},"agent_actions":{"view_html":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE","download_json":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE.json","view_paper":"https://pith.science/paper/FHZLSI4Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.05719&json=true","fetch_graph":"https://pith.science/api/pith-number/FHZLSI4Z5ET566QUEGAYWI34NE/graph.json","fetch_events":"https://pith.science/api/pith-number/FHZLSI4Z5ET566QUEGAYWI34NE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE/action/storage_attestation","attest_author":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE/action/author_attestation","sign_citation":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE/action/citation_signature","submit_replication":"https://pith.science/pith/FHZLSI4Z5ET566QUEGAYWI34NE/action/replication_record"}},"created_at":"2026-05-18T01:38:51.674089+00:00","updated_at":"2026-05-18T01:38:51.674089+00:00"}