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- W3114804054 abstract "The Grundy and the {rm b}-chromatic number of graphs are two important chromatic parameters. The Grundy number of a graph $G$, denoted by $Gamma(G)$ is the worst case behavior of greedy (First-Fit) coloring procedure for $G$ and the {rm b}-chromatic number ${rm{b}}(G)$ 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. This paper presents a comparative study of these coloring parameters. There exists a sequence ${G_n}_{ngeq 1}$ with limited {rm b}-chromatic number but $Gamma(G_n)rightarrow infty$. We obtain families of graphs $mathcal{F}$ such that for some adequate function $f(.)$, $Gamma(G)leq f({rm{b}}(G))$, for each graph $G$ from the family. This verifies a previous conjecture for these families." @default.
- W3114804054 created "2021-01-05" @default.
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- W3114804054 date "2020-12-18" @default.
- W3114804054 modified "2023-09-27" @default.
- W3114804054 title "On Grundy and b-chromatic number of some families of graphs: a comparative study." @default.
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