Mathematical Sciences: Faculty Publications
General Bounds on Rainbow Domination Numbers
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
Copyright
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