The Grundy and the 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 b-chromatic number \(\mathrm{{b}}(G)\) 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 \(\{G_n\}_{n\ge 1}\) with limited b-chromatic number but \(\Gamma (G_n)\rightarrow \infty \). We obtain families of graphs \({\mathcal {F}}\) such that for some adequate function f(.), \(\Gamma (G)\le f(\mathrm{{b}}(G))\), for each graph G from the family. This verifies a previous conjecture for these families.

图的Grundy和b色数是两个重要的色度参数。图的格伦迪数ģ，记\（\伽玛（G）\）是贪婪（初-FIT）的为最坏的情况行为着色过程ģ和b色数\（\ mathrm {{B}} （G）\）是在任何所使用的颜色的最大数量的颜色主导的着色ģ。由于这些着色剂的性质不同，因此在文献中对其进行了广泛的研究，但分别进行了研究。本文介绍了这些着色参数的比较研究。存在序列\（\ {G_n \} _ {n \ ge 1} \），其b色数有限，但是\（\ Gamma（G_n）\ rightarrow \ infty \）。我们获得图族\（{\ mathcal {F}} \），使得对于某些适当的函数f（。），\（\ Gamma（G）\ le f（\ mathrm {{b}}（G））\ ），针对家庭中的每个图G。这验证了这些家庭先前的猜想。