General Bounds on Rainbow Domination Numbers

Authors

Shinya Fujita, Maebashi Institute of Technology, Maebashi, JapanFollow
Michitaka Furuya, Tokyo University of ScienceFollow
Colton Magnant, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

5-2015

Publication Title

Graphs and Combinatorics

DOI

10.1007/s00373-013-1394-9

ISSN

1435-5914

Abstract

A k-rainbow dominating function of a graph G is a function f from the vertices V(G) to 2{1,2,…,k} such that, for all v∈V(G), either f(v)≠∅ or ⋃u∈N[v]f(u)={1,2,…,k}. The k-rainbow domination number of a graph G is then defined to be the minimum weight w(f)=∑v∈V(G)|f(v)| of a k-rainbow dominating function. In this work, we prove sharp upper bounds on the k-rainbow domination number for all values of k. Furthermore, we also consider the problem with minimum degree restrictions on the graph.

Recommended Citation

Fujita, Shinya, Michitaka Furuya, Colton Magnant. 2015. "General Bounds on Rainbow Domination Numbers." Graphs and Combinatorics, 31 (3): 601-613. doi: 10.1007/s00373-013-1394-9
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/582