论文标题
具有给定最大程度的图形的注入性边缘色
Injective edge-coloring of graphs with given maximum degree
论文作者
论文摘要
如果任何两个不同的边缘$ e_1 $ and $ e_2 $，图形$ g $的边缘的颜色是注入性的，如果$ e_1 $和$ e_2 $的颜色在$ g $中的距离$ 1 $或公共三角形。自然地，$ g $，$χ'_{inj}（g）$的注入性色素指数是$ g $的注射式边缘色所需的最小颜色数量。当我们对周长和/或色度为$ g $的限制时，我们研究了$ g $的$ g $的注入性色度指数的最大程度。我们还将边界与强色指数上的类似边界进行比较。
A coloring of edges of a graph $G$ is injective if for any two distinct edges $e_1$ and $e_2$, the colors of $e_1$ and $e_2$ are distinct if they are at distance $1$ in $G$ or in a common triangle. Naturally, the injective chromatic index of $G$, $χ'_{inj}(G)$, is the minimum number of colors needed for an injective edge-coloring of $G$. We study how large can be the injective chromatic index of $G$ in terms of maximum degree of $G$ when we have restrictions on girth and/or chromatic number of $G$. We also compare our bounds with analogous bounds on the strong chromatic index.
