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Caro and Yuster (Discrete Mathematics 310 (2010) 742-747) conjectured that, for every $k$, there is a constant $c_k$ such that $f_k(G)\\leq c_k \\sqrt{n(G)}$ for every graph $G$. Verifying a conjecture of Caro, Lauri, and Zarb (arXiv:1704.08472v1), we show the best possible result that, if $t$ is a positive integer, and $F$ is a forest of order at most $\\frac{1}{6}\\left(t^3+6t^2+17t+12\\right)$, "},"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":"1705.07409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-21T07:45:36Z","cross_cats_sorted":[],"title_canon_sha256":"a65b11719f0b5599063d3b41c801f77ea544ed58d676261a196ace2bbe4c461f","abstract_canon_sha256":"dc566380ee511d0a748357d58d32d55feed9b52b49505dcc59cb555b900a1e69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:05.687640Z","signature_b64":"R5irq6Uh9Q/nSGowiOg0NgL6AxgHc+dBLUDC4e3z43BhOBx6R75d7CPUchO6nZHkuqg/T/oAp6imjbsPNV97Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26fd12202374913bb08c4cc03e115768c5a71a30e37c700c66a1eac604c1cb70","last_reissued_at":"2026-05-18T00:44:05.687086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:05.687086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equating $k$ Maximum Degrees in Graphs without Short Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. 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