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A linear forest is a graph whose connected components are all paths and isolated vertices. In this paper, we let $\\mathcal{L}_n^k$ be the set of all linear forests of order $n$ with at least $n-k+1$ edges. We prove that when $n\\geq 3k$ and $k\\geq 2$, \\[ ex(n;\\mathcal{L}_n^k)=\\binom{n-k+"},"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":"1807.01825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-05T01:49:06Z","cross_cats_sorted":[],"title_canon_sha256":"3f4e1424b3fd8c2dd730a8a8484e5eff0ed0b12f6a15ab66832e50c27cea4d1b","abstract_canon_sha256":"5866fd2f61435159097de407bfd69ed060a110c3097c43499b6a406ace3109b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:28.567897Z","signature_b64":"daF6ktyWjDy3Q9FjVbL73lvzdw4a+1C5UfRFTT1Tit0vGKfdi5YIB52hMT0kBtqCviAHEojhOmsFD5C98zDpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a61584efa1c52a1e1241c478a2592588317f9da3863f26dc17697c37732b62ff","last_reissued_at":"2026-05-18T00:11:28.567340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:28.567340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tur\\'{a}n Number for Spanning Linear Forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jian Wang, Weihua Yang","submitted_at":"2018-07-05T01:49:06Z","abstract_excerpt":"For a set of graphs $\\mathcal{F}$, the extremal number $ex(n;\\mathcal{F})$ is the maximum number of edges in a graph of order $n$ not containing any subgraph isomorphic to some graph in $\\mathcal{F}$. 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