標題: On the number of rainbow spanning trees in edge-colored complete graphs
作者: Fu, Hung-Lin
Lo, Yuan-Hsun
Perry, K. E.
Rodger, C. A.
應用數學系
Department of Applied Mathematics
關鍵字: Edge-coloring;Complete graph;Rainbow spanning tree
公開日期: 1-八月-2018
摘要: A spanning tree of a properly edge-colored complete graph, K, 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 [root 6m+9/3] 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 spanning tree is determined in the process. This improves upon best constructive result to date in the literature which produces exactly three rainbow trees. (C) 2018 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.disc.2018.05.008
http://hdl.handle.net/11536/145260
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.05.008
期刊: DISCRETE MATHEMATICS
Volume: 341
起始頁: 2343
結束頁: 2352
顯示於類別:期刊論文