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We present new results concerning the minimum leaf number of cubic graphs: we show that if $G$ is a connected cubic graph of order $n$, then $\\mathrm{ml}(G) \\leq \\frac{n}6 + \\frac13$, improving on the best known result in [Inf. Process. Lett. 105 (2008) 164-169] and proving the conjecture in [Electron. J. Graph Theory and Applications 5 (2017) 207-211]. We further prove that if $G$ is also 2-connected, then $\\mathrm{ml}(G) \\leq \\frac{n}{6.53}$, improv"},"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":"1806.04451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-12T11:54:15Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"87d44e1e893f3dc23fbf1e99553c2b99eb0cd299daf5b828cd9fce1824642493","abstract_canon_sha256":"85c23244099fc123a061f0a37d57f1bb27ec131ba1c927553ee71fe1a20d74f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:35.486930Z","signature_b64":"qs8FQguW3ebFNW318IOlYbZohoHsPJEexLvaoT3QEtg/N1Fi7fnfDzgJsEDG5VAgsulx/dkZd1wbFvotRCsJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9043764cf241748d4679ff496cb87be399b9818cc8e0ed9dbf54673c545f23ad","last_reissued_at":"2026-05-18T00:13:35.486263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:35.486263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the minimum leaf number of cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"G\\'abor Wiener, Jan Goedgebeur, Kenta Ozeki, Nico Van Cleemput","submitted_at":"2018-06-12T11:54:15Z","abstract_excerpt":"The \\emph{minimum leaf number} $\\hbox{ml} (G)$ of a connected graph $G$ is defined as the minimum number of leaves of the spanning trees of $G$. 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