{"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. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02866","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}