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

12-1-2011

Publication Title

Electronic Notes in Discrete Mathematics

DOI

10.1016/j.endm.2011.09.059

ISSN

1571-0653

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 rck(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 rck(G) for complete bipartite and multipartite graphs, highly connected graphs, and random graphs.

Recommended Citation

Fujita, Shinya, Henry Liu, Colton Magnant. 2011. "Rainbow K-Connection In Dense Graphs." Electronic Notes in Discrete Mathematics, 38 (1): 361-366. doi: 10.1016/j.endm.2011.09.059
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/113