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If $G$ is a plane graph, then a facial nonrepetitive vertex coloring of $G$ is a vertex coloring such that any facial path is nonrepetitive. Let $\\pi_f(G)$ denote the minimum number of colors of a facial nonrepetitive vertex coloring of $G$. Jendro\\vl and Harant posed a conjecture that $\\pi_f(G)$ can be bounded "},"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":"1105.1023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-05T09:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"da325d1fa775fb2420f15ccb5118bb97854b7737ed5160b5d881965b8491b97f","abstract_canon_sha256":"f02efa066527c5e758d099084f71e3ac60be407691a8e25d56a5442a9301df04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:18.656328Z","signature_b64":"67gXrBVvJ+qCVWPy22Zj7/YYV8utaRKlwsJjHSsqz22chBQzfBSdwFGVSY5CwArG3iCk0X/likXRYwwxafvNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5363d664c541e98d97e7d61ad7aef16d1a15e5d160e1bf1e65cd23a83ceb2338","last_reissued_at":"2026-05-18T03:46:18.655341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:18.655341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex coloring of plane graphs with nonrepetitive boundary paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J\\'anos Bar\\'at, J\\'ulius Czap","submitted_at":"2011-05-05T09:41:59Z","abstract_excerpt":"A sequence $s_1,s_2,...,s_k,s_1,s_2,...,s_k$ is a repetition. A sequence $S$ is nonrepetitive, if no subsequence of consecutive terms of $S$ form a repetition. Let $G$ be a vertex colored graph. A path of $G$ is nonrepetitive, if the sequence of colors on its vertices is nonrepetitive. If $G$ is a plane graph, then a facial nonrepetitive vertex coloring of $G$ is a vertex coloring such that any facial path is nonrepetitive. Let $\\pi_f(G)$ denote the minimum number of colors of a facial nonrepetitive vertex coloring of $G$. Jendro\\vl and Harant posed a conjecture that $\\pi_f(G)$ can be bounded "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1023","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":"1105.1023","created_at":"2026-05-18T03:46:18.655526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1023v1","created_at":"2026-05-18T03:46:18.655526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1023","created_at":"2026-05-18T03:46:18.655526+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNR5MZGFIHUY","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNR5MZGFIHUY3F7H","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNR5MZGF","created_at":"2026-05-18T12:26:32.869790+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/KNR5MZGFIHUY3F7H2YNNPLXRNU","json":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU.json","graph_json":"https://pith.science/api/pith-number/KNR5MZGFIHUY3F7H2YNNPLXRNU/graph.json","events_json":"https://pith.science/api/pith-number/KNR5MZGFIHUY3F7H2YNNPLXRNU/events.json","paper":"https://pith.science/paper/KNR5MZGF"},"agent_actions":{"view_html":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU","download_json":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU.json","view_paper":"https://pith.science/paper/KNR5MZGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1023&json=true","fetch_graph":"https://pith.science/api/pith-number/KNR5MZGFIHUY3F7H2YNNPLXRNU/graph.json","fetch_events":"https://pith.science/api/pith-number/KNR5MZGFIHUY3F7H2YNNPLXRNU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/action/storage_attestation","attest_author":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/action/author_attestation","sign_citation":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/action/citation_signature","submit_replication":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/action/replication_record"}},"created_at":"2026-05-18T03:46:18.655526+00:00","updated_at":"2026-05-18T03:46:18.655526+00:00"}