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We say that a set of $n$ lines $\\mathcal{L}$ is universal for trees if for any tree $T$ and any bijection $\\iota$ there exists such an embedding. We prove that any sufficiently big set of lines is not universal for trees, which solves an open problem asked by Dujmovic et al."},"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":"1104.1307","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-07T11:56:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f68f7eab8b0d0ae571d4abb5e05b23b1ba79a0d32f9457e9873330e46d9e979","abstract_canon_sha256":"bd1dc9b41f7c5325af715fac5c3a88b40ca55ca227733b774e5779f7b7160801"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:10.555962Z","signature_b64":"OtKZ6Ql26RboYJPCcwbWzHN8oyf2+veOVAd8X65c1VDY8MzbUCt8GC2oqHIeCZ6Sj+xZBFmZD79buxIcFtzDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7de10c7eb9b93a6baa6bc3ae4096501eae74040bc77ced174f3a54c7a7f4b8ab","last_reissued_at":"2026-05-18T02:22:10.555195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:10.555195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Sets of Lines Not-Supporting Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Daniel Neuwirth, Radoslav Fulek","submitted_at":"2011-04-07T11:56:39Z","abstract_excerpt":"We study the following problem introduced by Dujmovic et al. 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