{"paper":{"title":"On Edge-Partitioning of Complete Geometric Graphs into Plane Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adem Kilicman, Gek L. Chia, Hazim Michman Trao, Niran Abbas Ali","submitted_at":"2019-06-13T10:56:13Z","abstract_excerpt":"In response to a well-known open question ``Does every complete geometric graph on $2n\\/$ vertices have a partition of its edge set into $n\\/$ plane spanning trees?\" we provide an affirmative answer when the complete geometry graph is in the regular wheel configuration. Also we present sufficient conditions for the complete geometric graph on $2n\\/$ vertices to have a partition of its edge set into $n\\/$ plane spanning trees (which are double stars, caterpillars or $ w\\/$-caterpillars)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05598","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"}