EQUITABLE DEFECTIVE COLORINGS OF COMPLETE BIPARTITE GRAPHS
Kittikorn Nakprasit, S. Cummuang · International Journal of Pure and Apllied Mathematics · 2014
A graph G has an equitable k-defective coloring in m colors if its vertices can be colored with m colors such that the maximum degree of any subgraph induced by vertices assigned to the same color is at most k and the numbers of vertices in any two sets composed of the vertices that are assigned to the same color differ by at most one.The equitable k-defective chromatic number of a graph G, denoted by χ ED,k (G), is the smallest positive integer m for which G has an equitable k-defective coloring in m colors.In this paper, we present the equitable k-defective chromatic numbers of complete bipartite graphs for k = 1 and k = 2.