{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SW3F75HABULTG67XYYQA3XONDY","short_pith_number":"pith:SW3F75HA","schema_version":"1.0","canonical_sha256":"95b65ff4e00d17337bf7c6200dddcd1e2281d15363f4db4a74e9b9bdd174849f","source":{"kind":"arxiv","id":"2606.12093","version":1},"attestation_state":"computed","paper":{"title":"Extremal number of edges in graphs without homeomorphically irreducible spanning trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huiqing Liu, Xiaolan Hu, Yibo Li","submitted_at":"2026-06-10T13:52:21Z","abstract_excerpt":"For integers $k\\ge 1$ and $n\\ge k+1$, let $\\operatorname{ex}^{\\mathrm{HIST}}_k(n)$ denote the maximum number of edges in a $k$-connected graph of order $n$ which contains no homeomorphically irreducible spanning tree (or briefly HIST). We determine these extremal numbers for $k=1$ and $k=2$. More precisely, we prove that $\\operatorname{ex}^{\\mathrm{HIST}}_1(n)=\\binom{n-2}{2}+2$ for $n\\ge 9$, with $L_n$ as the unique extremal graph, and that $\\operatorname{ex}^{\\mathrm{HIST}}_2(n)=\\binom{n-3}{2}+4$ for $n\\ge 13$, with $B_n$ as the unique extremal graph. This provides a Tur\\'an-type extremal res"},"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":"2606.12093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T13:52:21Z","cross_cats_sorted":[],"title_canon_sha256":"3b8fb8ff1ac0c8cc7f0bbc4774c22d0ae2c439d8e76498f50f0dcc0410205be3","abstract_canon_sha256":"dd5ee4366f19e2bd028b35c470e29cf3d6a04a772dd3f47ccb870bc4af77f943"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:47.817795Z","signature_b64":"YW+bToW/k9nDOOghp2hRjjRc71FJor1z8vj3s2+QEF7AGR/43DA9eirY46bjCusiPegJdcqFfeuPwysAYKrqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b65ff4e00d17337bf7c6200dddcd1e2281d15363f4db4a74e9b9bdd174849f","last_reissued_at":"2026-06-11T01:10:47.816910Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:47.816910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal number of edges in graphs without homeomorphically irreducible spanning trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huiqing Liu, Xiaolan Hu, Yibo Li","submitted_at":"2026-06-10T13:52:21Z","abstract_excerpt":"For integers $k\\ge 1$ and $n\\ge k+1$, let $\\operatorname{ex}^{\\mathrm{HIST}}_k(n)$ denote the maximum number of edges in a $k$-connected graph of order $n$ which contains no homeomorphically irreducible spanning tree (or briefly HIST). We determine these extremal numbers for $k=1$ and $k=2$. More precisely, we prove that $\\operatorname{ex}^{\\mathrm{HIST}}_1(n)=\\binom{n-2}{2}+2$ for $n\\ge 9$, with $L_n$ as the unique extremal graph, and that $\\operatorname{ex}^{\\mathrm{HIST}}_2(n)=\\binom{n-3}{2}+4$ for $n\\ge 13$, with $B_n$ as the unique extremal graph. 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