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- Title
General Bounds on Rainbow Domination Numbers.
- Authors
Fujita, Shinya; Furuya, Michitaka; Magnant, Colton
- Abstract
A k-rainbow dominating function of a graph G is a function f from the vertices V( G) to $${2^{\{1, 2, \dots, k\}}}$$ such that, for all $${v \in V(G)}$$ , either $${f(v) \neq \emptyset}$$ or $${\bigcup_{u \in N[v]} f(u) = \{1, 2, \dots, k\}}$$ . The k-rainbow domination number of a graph G is then defined to be the minimum weight $${w(f) = \sum_{v \in V(G)} |f(v)|}$$ 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.
- Subjects
NUMBER theory; SET theory; GEOMETRIC vertices; MATHEMATICAL functions; MATHEMATICAL analysis
- Publication
Graphs & Combinatorics, 2015, Vol 31, Issue 3, p601
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-013-1394-9