论文标题
与Edge-List彩色和总色数字相关的界限
Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph
论文作者
论文摘要
我们表明，对于简单的图形，$ g $，$ c'（g）\leqΔ（g）+2 $其中$ c'（g）$是$ g $的选择索引（或边缘上的色度数），而$δ（g）$是$ g $的最大程度。 作为此结果的简单推论，我们表明，简单图的总色数$χ_t（g）$满足不平等的$χ_t（g）\ leq \δ（g）+4 $，总选择数量$ c_t（g）$也满足了这种不平等。 我们还将这些边界与简单图的霍尔指数和大厅条件索引以及简单图的总霍尔条件数量相关联。
We show that for a simple graph $G$, $c'(G)\leqΔ(G)+2$ where $c'(G)$ is the choice index (or edge-list chromatic number) of $G$, and $Δ(G)$ is the maximum degree of $G$. As a simple corollary of this result, we show that the total chromatic number $χ_T(G)$ of a simple graph satisfies the inequality $χ_T(G)\leq\ Δ(G)+4$ and the total choice number $c_T(G)$ also satisfies this inequality. We also relate these bounds to the Hall index and the Hall condition index of a simple graph, and to the total Hall number and the total Hall condition number of a simple graph.
