BibTeX

@article{SCRCTGABNO22,
	author	 = {Zoya Masih and Manouchehr Zaker},
	title	 = {{Some comparative results concerning the Grundy and b-chromatic number of graphs}},
	year	 = {2022},
	month	 = {01},
	publisher	 = {Elsevier},
	journal	 = {Discrete Applied Mathematics},
	pages	 = {1-6},
	issn	 = {0166-218X},
	doi	 = {https://doi.org/10.1016/j.dam.2021.09.015},
	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 b(G) is the maximum number of colors used in any color-dominating coloring of G. Because the nature of these colorings are different they have been studied widely but separately in the literature. In this paper we first prove that Γ(G)−⌈logΓ(G)⌉≤b(G), if the girth of G is sufficiently large with respect to its maximum degree. Next, we prove that if G is K2,3-free then Γ(G)≤(b(G))3/2. These results confirm a previous conjecture for these families of graphs.},
	url	 = {https://www.sciencedirect.com/science/article/abs/pii/S0166218X21003905},
}