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We show that for any bridge-addable, monotone class A whose elements have vertex set 1,...,n, the probability that a uniformly random element of A is connected is at least (1-o_n(1)) e^{-1/2}, where o_n(1) tends to zero as n tends to infinity. This establishes the special case of a conjecture of McDiarmid, Stege"},"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":"1110.0009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-30T20:07:37Z","cross_cats_sorted":[],"title_canon_sha256":"194e46e437224c03c37e0842110c156f3c425f7e98bc58077580ecb3dd48cb5d","abstract_canon_sha256":"76bb05a65754a09ddd80cad4adaab13644eefa8957fd6e5b2805251ef30a99af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:50.995311Z","signature_b64":"cVw4oUXW7YlZ6TkVew0k+lt+sRS3HSw0ZOrjn9z6X9QGm2QjWEHxjVnyJHR7J7Jai/NbX05tFPGttlE3hRCCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beac9dde71dfe4f9b1c8099a21fd79e023e30a7ccbd15f4ed773ef4aa95742bc","last_reissued_at":"2026-05-18T04:11:50.994738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:50.994738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectivity for bridge-addable monotone graph classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce Reed, Colin McDiarmid, Louigi Addario Berry","submitted_at":"2011-09-30T20:07:37Z","abstract_excerpt":"A class A of labelled graphs is bridge-addable if for all graphs G in A and all vertices u and v in distinct connected components of G, the graph obtained by adding an edge between u and u is also in A; the class A is monotone if for all G in A and all subgraphs H of G, H is also in A. 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