author	 = {Zoya Masih},
	title	 = {{On comparative results concerning the Grundy and b-chromatic number of graphs}},
	advisors	 = {[[|Manouchehr Zaker]]},
	year	 = {2021},
	month	 = {10},
	school	 = {Universität Hamburg},
	type	 = {PhD Thesis},
	abstract	 = {The Grundy and b-chromatic number of graphs are two important chromatic parameters. The Grundy number of a graph G, denoted by Γ(G) is the worst case behavior of greedy (First-Fit) coloring procedure for G and the b-chromatic number, denoted by b(G), is the maximum number of colors used in any color-dominating coloring of G. Since the nature of these colorings are different, they have been studied widely but separately in the literature. This dissertation firstly presents some preliminary concepts. Then the two chromatic numbers are compared for Trees, Cacti, (K4,C4)-free graphs and K2q-free graphs. In each family, a function f will be introduced, such that, for every graph G of the family, the inequality Γ(G)≤f(b(G)) holds. The aforesaid function, is also presented for graphs with sufficiently large girth.},