{"paper":{"title":"On the Number of Rainbow Spanning Trees in Edge-Colored Complete Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. A. Rodger, Hung-Lin Fu, K. E. Perry, Yuan-Hsun Lo","submitted_at":"2016-05-15T06:45:45Z","abstract_excerpt":"A spanning tree of a properly edge-colored complete graph, $K_n$, is rainbow provided that each of its edges receives a distinct color. In 1996, Brualdi and Hollingsworth conjectured that if $K_{2m}$ is properly $(2m-1)$-edge-colored, then the edges of $K_{2m}$ can be partitioned into $m$ rainbow spanning trees except when $m=2$. By means of an explicit, constructive approach, in this paper we construct $\\lfloor \\sqrt{6m+9}/3 \\rfloor$ mutually edge-disjoint rainbow spanning trees for any positive value of $m$. Not only are the rainbow trees produced, but also some structure of each rainbow spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04501","kind":"arxiv","version":2},"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"}