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We show that if $2\\le |B|\\le \\sum_{x\\in R}(f(x)-2) + 2$, then there exists a non-crossing geometric spanning tree $T$ on $R\\cup B$ such that $2\\le \\operatorname{deg}_T(x)\\le f(x)$ for every $x\\in R$ and the set of leaves of $T$ is $B$, where every edge of $T$ is a straight-line segment."},"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":"1812.02866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-12-07T01:17:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"31f99b1d3ae2cdfcd9a9fcec3c558dd8fbbe9998320e460f277b9e985b676b9c","abstract_canon_sha256":"9fe97406c8a7002f80c01d78d9cb160019289ed564c19250f922acb25824593a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:51.619178Z","signature_b64":"eDmeMIdH0xgpdpREW9jj1xkCcqh5fu2h3Ctz3eVlUjkTnIjqce1NndP8CE3m8EM7PAER1uRTzowkyQyLmMIxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b50f2eb650a1a6ff31d95f4709e97ade514c552b08850f4eed8ada5dcf53c38","last_reissued_at":"2026-05-17T23:58:51.618522Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:51.618522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-crossing geometric spanning trees with bounded degree and monochromatic leaves on bicolored point sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"David Orden, Kenta Noguchi, Mikio Kano","submitted_at":"2018-12-07T01:17:36Z","abstract_excerpt":"Let $R$ and $B$ be a set of red points and a set of blue points in the plane, respectively, such that $R\\cup B$ is in general position, and let $f:R \\to \\{2,3,4, \\ldots \\}$ be a function. 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