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}, }