K-Rainbow Domatic Numbers

Authors

Shinya Fujita, Maebashi Institute of TechnologyFollow
Michitaka Furuya, Tokyo Universtiy of ScienceFollow
Colton Magnant, Georgia Southern UniversityFollow

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 d_rk(G) is the maximum integer d such that there exists a set of k-rainbow dominating functions f₁,f₂,…,f_d 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.

Recommended Citation

Fujita, Shinya, Michitaka Furuya, Colton Magnant. 2012. "K-Rainbow Domatic Numbers." Discrete Applied Mathematics, 160 (7-8): 1104-1113. doi: 10.1016/j.dam.2012.01.010
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/110