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Here, we consider $F$-WORM colorings with a fixed 2-connected graph $F$ and prove the following three main results: (1) For every natural number $k$, there exists a graph $G$ which is $F$-WORM colorable and $W^-(G,F)=k$; (2) It is NP-complete to decide whether a graph is $F$-WORM colorable"},"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":"1512.00478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-01T21:04:07Z","cross_cats_sorted":[],"title_canon_sha256":"1cf27c60547508ecbf3e5272ef3b6c999d2dcb5e2717064e403d9be262b0991d","abstract_canon_sha256":"a0a5230a11d48e29bf950dbd719c4c39884454579e88e90225bfa296d1acce61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:25.828626Z","signature_b64":"nxLf5l6B0Fzyqchxj69Zy8ZQj8hd4XlAJq+QUqV7TZxzkdQ4ZcKrQWE3yjrb6sxzArXIYrszELBBoAVCUk0dBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39da4451faa15c9df86d49ec0ac650be9a0777972fc5e4b2e84053462c3ca43c","last_reissued_at":"2026-05-18T01:25:25.828113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:25.828113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$F$-WORM colorings: Results for 2-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as, Zsolt Tuza","submitted_at":"2015-12-01T21:04:07Z","abstract_excerpt":"Given two graphs $F$ and $G$, an $F$-WORM coloring of $G$ is an assignment of colors to its vertices in such a way that no $F$-subgraph of $G$ is monochromatic or rainbow. If $G$ has at least one such coloring, then it is called $F$-WORM colorable and $W^-(G,F)$ denotes the minimum possible number of colors. Here, we consider $F$-WORM colorings with a fixed 2-connected graph $F$ and prove the following three main results: (1) For every natural number $k$, there exists a graph $G$ which is $F$-WORM colorable and $W^-(G,F)=k$; (2) It is NP-complete to decide whether a graph is $F$-WORM colorable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00478","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":"1512.00478","created_at":"2026-05-18T01:25:25.828189+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00478v1","created_at":"2026-05-18T01:25:25.828189+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00478","created_at":"2026-05-18T01:25:25.828189+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHNEIUP2UFOJ","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHNEIUP2UFOJ36DN","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHNEIUP2","created_at":"2026-05-18T12:29:25.134429+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/HHNEIUP2UFOJ36DNJHWAVRSQX2","json":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2.json","graph_json":"https://pith.science/api/pith-number/HHNEIUP2UFOJ36DNJHWAVRSQX2/graph.json","events_json":"https://pith.science/api/pith-number/HHNEIUP2UFOJ36DNJHWAVRSQX2/events.json","paper":"https://pith.science/paper/HHNEIUP2"},"agent_actions":{"view_html":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2","download_json":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2.json","view_paper":"https://pith.science/paper/HHNEIUP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00478&json=true","fetch_graph":"https://pith.science/api/pith-number/HHNEIUP2UFOJ36DNJHWAVRSQX2/graph.json","fetch_events":"https://pith.science/api/pith-number/HHNEIUP2UFOJ36DNJHWAVRSQX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2/action/storage_attestation","attest_author":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2/action/author_attestation","sign_citation":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2/action/citation_signature","submit_replication":"https://pith.science/pith/HHNEIUP2UFOJ36DNJHWAVRSQX2/action/replication_record"}},"created_at":"2026-05-18T01:25:25.828189+00:00","updated_at":"2026-05-18T01:25:25.828189+00:00"}