#### Title

Rainbow K-Connection in Dense Graphs

#### Document Type

Article

#### Publication Date

5-2015

#### Publication Title

Journal of Combinatorial Mathematics and Combinatorial Computing

#### ISSN

0835-3026

#### Abstract

An edge-colouring of a graph *G* is *rainbow k-connected* if, for any two vertices of *G*, there are *k* internally vertex-disjoint paths joining them, each of which is *rainbow* (i.e., all edges of each path have distinct colours). The minimum number of colours for which there exists a rainbow *k*-connected colouring for *G* is the *rainbow k-connection number* of *G*, and is denoted by rc_{k}(*G*). The function rc_{k}(*G*) was introduced by Chartrand et al. in 2008, and has since attracted considerable interest. In this note, we shall consider the function rc_{k}(*G*) for complete bipartite and multipartite graphs, highly connected graphs, and random graphs.

#### Recommended Citation

Fujita, Shinya, Henry Liu, Colton Magnant.
2015.
"Rainbow K-Connection in Dense Graphs."
*Journal of Combinatorial Mathematics and Combinatorial Computing*, 93: 33-52.

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/372