Rainbow K-Connection in Dense Graphs

Authors

Shinya Fujita, Maebashi Institute of TechnologyFollow
Henry Liu, Universidade Nova de Lisboa Quinta da TorreFollow
Colton Magnant, Georgia Southern UniversityFollow

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