Title

K-Rainbow Domatic Numbers

Document Type

Article

Publication Date

5-2012

Publication Title

Discrete Applied Mathematics

DOI

10.1016/j.dam.2012.01.010

ISSN

0166-218X

Abstract

A k-rainbow dominating function of a graph is a function f from the vertices V(G) to 2[k] such that, for allv∈V(G), either f(v)≠0̸ or ⋃u∈N[v]f(u)={1,…,k}. The k-rainbow domatic number drk(G) is the maximum integer d such that there exists a set of k-rainbow dominating functions f1,f2,…,fd with for all v∈V(G). We study thek-rainbow domatic number by finding this number for some classes of graphs and improving upon some known general bounds.

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