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The topological space |G| is n-arc connected (n-ac) if every set of no more than n points of |G| are contained in an arc (a homeomorphic copy of the closed unit interval).\n  For any graph G, we show the following are equivalent: (i) |G| in 7-ac, (ii) |G| is n-ac for all n, and (iii) G is a subdivision of one of nine graphs. A graph G has |G| 6-ac if and only if either G is one of the nine 7-ac graphs, or, after suppressing all degree-2-vertices, the graph G is 3-regular, 3-connect"},"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":"1801.00179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T19:08:38Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"8d417732f7e9c830caaa485ec9b5e93d1cce3bd51a397651a85b3a890e556ef3","abstract_canon_sha256":"d29e378f6252d58e46bc67dd21551c1595adc7e4106c6b5409e1c6100f873448"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:34.140194Z","signature_b64":"XU+5zT6nBMYstFF9SBdjK9d+YVPihNMlXpMHQcWLmwZmp2paJWOtTSRZsIFjIn0TLGzD5WVapoNjXEDnvG0mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96e1bd5818670f12aa11a99cc279e062a7648c676b1b777e996dd71b39a4eca5","last_reissued_at":"2026-05-18T00:14:34.139637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:34.139637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"n-Arc Connected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CO","authors_text":"Ana Mamatelashvili, Max Pitz, Paul Gartside","submitted_at":"2017-12-30T19:08:38Z","abstract_excerpt":"Given a graph G, of arbitrary size and unbounded vertex degree, denote by |G| the one-complex associated with $G$. 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A graph G has |G| 6-ac if and only if either G is one of the nine 7-ac graphs, or, after suppressing all degree-2-vertices, the graph G is 3-regular, 3-connect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00179","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":"1801.00179","created_at":"2026-05-18T00:14:34.139736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00179v2","created_at":"2026-05-18T00:14:34.139736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00179","created_at":"2026-05-18T00:14:34.139736+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3Q32WAYM4HR","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3Q32WAYM4HRFKQR","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3Q32WAY","created_at":"2026-05-18T12:31:43.269735+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/S3Q32WAYM4HRFKQRVGOME6PAMK","json":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK.json","graph_json":"https://pith.science/api/pith-number/S3Q32WAYM4HRFKQRVGOME6PAMK/graph.json","events_json":"https://pith.science/api/pith-number/S3Q32WAYM4HRFKQRVGOME6PAMK/events.json","paper":"https://pith.science/paper/S3Q32WAY"},"agent_actions":{"view_html":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK","download_json":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK.json","view_paper":"https://pith.science/paper/S3Q32WAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00179&json=true","fetch_graph":"https://pith.science/api/pith-number/S3Q32WAYM4HRFKQRVGOME6PAMK/graph.json","fetch_events":"https://pith.science/api/pith-number/S3Q32WAYM4HRFKQRVGOME6PAMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/action/storage_attestation","attest_author":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/action/author_attestation","sign_citation":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/action/citation_signature","submit_replication":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/action/replication_record"}},"created_at":"2026-05-18T00:14:34.139736+00:00","updated_at":"2026-05-18T00:14:34.139736+00:00"}