2013/10/10 by Qingqiong Cai, Xueliang Li, Cai, Qingqiong +3 · 1 citation
Mathematics · #05C05 #05C15 #05C80 #05D40 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C05 #msc:05C15 #msc:05C80 #msc:05D40
paper · pdf · doi:10.48550/arxiv.1310.2783
13 pages. arXiv admin note: substantial text overlap with arXiv:1212.6845
arxiv created 2013/10/18 · arxiv updated 2013/10/21
A tree in an edge-colored graph G is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers k, ℓ with k≥ 3, the (k,ℓ)-rainbow index rxk,ℓ(G) of G is the minimum number of colors needed in an edge-coloring of G such that for any set S of k vertices of G, there exist ℓ internally disjoint rainbow trees connecting S. This concept was introduced by Chartrand et al., and there have been very few results about it. In this paper, we investigate the (k,ℓ)-rainbow index for complete bipartite graphs and complete multipartite graphs. Some asymptotic values of their (k,ℓ)-rainbow index are obtained.