论文标题
关于Grundy和$ {\ rm B} $的注释 - 图形数字
A note concerning the Grundy and ${\rm b}$-chromatic number of graphs
论文作者
论文摘要
图$ g $的grundy数量是$ g $的首先颜色使用的最大颜色数，并用$γ（g）$表示。同样，$ {\ rm b} $ - 色度$ {\ rm {b}}（g）$ g $的$表达了另一种众所周知的着色过程的最坏情况，即$ g $的颜色为颜色。我们获得了一些图形系列$ \ MATHCAL {f} $，其中存在一个函数$ f（x）$，因此每个图$ f（g）\ leq f（{\ rm {b}}（g）（g））$ for家族中的每个图$ g $。致电任何此类家庭$（γ，b）$ - 有限的家庭。我们猜想$ {\ rm b} $的家族 - 单调图是$（γ，b）$ - 有限的，并验证了某些图形家庭的猜想。
The Grundy number of a graph $G$ is the maximum number of colors used by the First-Fit coloring of $G$ and is denoted by $Γ(G)$. Similarly, the ${\rm b}$-chromatic number ${\rm{b}}(G)$ of $G$ expresses the worst case behavior of another well-known coloring procedure i.e. color-dominating coloring of $G$. We obtain some families of graphs $\mathcal{F}$ for which there exists a function $f(x)$ such that $Γ(G)\leq f({\rm{b}}(G))$, for each graph $G$ from the family. Call any such family $(Γ,b)$-bounded family. We conjecture that the family of ${\rm b}$-monotone graphs is $(Γ,b)$-bounded and validate the conjecture for some families of graphs.
