论文标题
关于某些图的格伦迪和b-chromation数量：比较研究
On Grundy and b-chromatic number of some families of graphs: a comparative study
论文作者
论文摘要
Grundy和{\ rm B} -Chromation图数是两个重要的色度参数。 $γ（g）$表示的图形$ g $的Grundy数量是$ g $的贪婪（先进）着色过程的最坏情况，{\ rm b} - chrostic number $ {\ rm {b}}（b}}（g）（g）$是$ g $ $ g $的最大颜色。由于这些着色的性质不同，因此在文献中进行了广泛的研究。本文介绍了这些着色参数的比较研究。存在一个序列$ \ {g_n \} _ {n \ geq 1} $，limited {\ rm b} -cromatic数字，但$γ（g_n）\ rightarrow \ infty \ infty $。我们获得了图的家庭$ \ MATHCAL {f} $，因此对于某些适当的函数$ f（。）$，$γ（g）\ leq f（{\ rm {b}}（g）（g））$，对于家族的每个图$ g $。这验证了这些家庭以前的猜想。
The Grundy and the {\rm 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 {\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 $\{G_n\}_{n\geq 1}$ with limited {\rm b}-chromatic number but $Γ(G_n)\rightarrow \infty$. We obtain families of graphs $\mathcal{F}$ such that for some adequate function $f(.)$, $Γ(G)\leq f({\rm{b}}(G))$, for each graph $G$ from the family. This verifies a previous conjecture for these families.
