{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:C3Q3EODW2MISJOUUPWEUVLRP55","short_pith_number":"pith:C3Q3EODW","schema_version":"1.0","canonical_sha256":"16e1b23876d31124ba947d894aae2fef62b38627a0648d7e4b114718b90fa0af","source":{"kind":"arxiv","id":"1803.04889","version":1},"attestation_state":"computed","paper":{"title":"Planar anti-Ramsey numbers of matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gang Chen, Yongxin Lan, Zi-Xia Song","submitted_at":"2018-03-13T15:38:57Z","abstract_excerpt":"Given a positive integer $n$ and a planar graph $H$, let $\\mathcal{T}_n(H)$ be the family of all plane triangulations $T$ on $n$ vertices such that $T$ contains a subgraph isomorphic to $H$. The planar anti-Ramsey number of $H$, denoted $ar_{_\\mathcal{P}}(n, H)$, is the maximum number of colors in an edge-coloring of a plane triangulation $T\\in \\mathcal{T}_n(H)$ such that $T$ contains no rainbow copy of $H$. In this paper we study planar anti-Ramsey numbers of matchings. For all $t\\ge1$, let $M_t$ denote a matching of size $t$. We prove that for all $t\\ge6$ and $n\\ge 3t-6$, $2n+3t-15\\le ar_{_{"},"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":"1803.04889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-13T15:38:57Z","cross_cats_sorted":[],"title_canon_sha256":"dda275928944261a76370ed9d3ca1a953ef91df421f3f8d5d68117fb9a9b86bf","abstract_canon_sha256":"6b77e7ea049518f91a0cdf0a0a2e13eab51851df484da7c3d4f019b9b878f8d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:15.519125Z","signature_b64":"gaKydtYkV2tXinySXANL9Uz+zc3JSEpRQG3QFyQDZXqe+0WwKraeUJMKMwmEkF+xSp/1Pd1gh50Nl3Hr7KnJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e1b23876d31124ba947d894aae2fef62b38627a0648d7e4b114718b90fa0af","last_reissued_at":"2026-05-18T00:21:15.518693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:15.518693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Planar anti-Ramsey numbers of matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gang Chen, Yongxin Lan, Zi-Xia Song","submitted_at":"2018-03-13T15:38:57Z","abstract_excerpt":"Given a positive integer $n$ and a planar graph $H$, let $\\mathcal{T}_n(H)$ be the family of all plane triangulations $T$ on $n$ vertices such that $T$ contains a subgraph isomorphic to $H$. The planar anti-Ramsey number of $H$, denoted $ar_{_\\mathcal{P}}(n, H)$, is the maximum number of colors in an edge-coloring of a plane triangulation $T\\in \\mathcal{T}_n(H)$ such that $T$ contains no rainbow copy of $H$. In this paper we study planar anti-Ramsey numbers of matchings. For all $t\\ge1$, let $M_t$ denote a matching of size $t$. We prove that for all $t\\ge6$ and $n\\ge 3t-6$, $2n+3t-15\\le ar_{_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04889","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":"1803.04889","created_at":"2026-05-18T00:21:15.518769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.04889v1","created_at":"2026-05-18T00:21:15.518769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04889","created_at":"2026-05-18T00:21:15.518769+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3Q3EODW2MIS","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3Q3EODW2MISJOUU","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3Q3EODW","created_at":"2026-05-18T12:32:16.446611+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/C3Q3EODW2MISJOUUPWEUVLRP55","json":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55.json","graph_json":"https://pith.science/api/pith-number/C3Q3EODW2MISJOUUPWEUVLRP55/graph.json","events_json":"https://pith.science/api/pith-number/C3Q3EODW2MISJOUUPWEUVLRP55/events.json","paper":"https://pith.science/paper/C3Q3EODW"},"agent_actions":{"view_html":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55","download_json":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55.json","view_paper":"https://pith.science/paper/C3Q3EODW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.04889&json=true","fetch_graph":"https://pith.science/api/pith-number/C3Q3EODW2MISJOUUPWEUVLRP55/graph.json","fetch_events":"https://pith.science/api/pith-number/C3Q3EODW2MISJOUUPWEUVLRP55/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55/action/storage_attestation","attest_author":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55/action/author_attestation","sign_citation":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55/action/citation_signature","submit_replication":"https://pith.science/pith/C3Q3EODW2MISJOUUPWEUVLRP55/action/replication_record"}},"created_at":"2026-05-18T00:21:15.518769+00:00","updated_at":"2026-05-18T00:21:15.518769+00:00"}