@article{Alon2003FactorDC,
title={Factor d-domatic colorings of graphs},
author={Noga Alon and Guillaume Fertin and Arthur L. Liestman and Thomas C. Shermer and Ladislav Stacho},
journal={Discrete Mathematics},
year={2003},
volume={262},
pages={17-25}
}

Consider a graph and a collection of (not necessarily edge-disjoint) connected spanning subgraphs (factors) of the graph. We consider the problem of coloring the vertices of the graph so that each color class of the vertices dominates each factor. We 5nd upper and lower bounds on (t; k), which we de5ne as the minimum radius of domination d such that every graph with a collection of k factors can be vertex colored with t colors so that each color class d-dominates each factor. It is perhaps… CONTINUE READING