论文标题
$ 2 $ - 距离，注入和精确的正方形列表色，具有最高度4的平面图
$2$-distance, injective, and exact square list-coloring of planar graphs with maximum degree 4
论文作者
论文摘要
在过去的各种基于平面图的基于距离的着色。我们将重点转移到其中的三个，即$ 2 $持续着色，注入性着色和精确的正方形着色。 $ 2 $持续的颜色是顶点的适当着色，在该顶点中，$ 2 $的两个顶点$ 2 $都会获得相同的颜色，注入性的着色是顶点的着色，在该顶点中，没有两个带有共同邻居的顶点的顶点获得相同的颜色，并且精确的正方形是在距离上的两种颜色的颜色，距离$ 2 $ $ 2 $ $ 2 $。我们证明，具有最高度的平面图$δ= 4 $，至少$ 4 $是$ 2 $ distance List $（δ+ 7）$ - 可颜色和浸润性清单$（δ+ 5）$ - 可着色。此外，我们证明具有$δ= 4 $的平面图是榜首$（δ+ 7）$ - 可着色和精确的正方形列表$（δ+ 6）$ - 可着色。
In the past various distance based colorings on planar graphs were introduced. We turn our focus to three of them, namely $2$-distance coloring, injective coloring, and exact square coloring. A $2$-distance coloring is a proper coloring of the vertices in which no two vertices at distance $2$ receive the same color, an injective coloring is a coloring of the vertices in which no two vertices with a common neighbor receive the same color, and an exact square coloring is a coloring of the vertices in which no two vertices at distance exactly $2$ receive the same color. We prove that planar graphs with maximum degree $Δ= 4$ and girth at least $4$ are $2$-distance list $(Δ+ 7)$-colorable and injectively list $(Δ+ 5)$-colorable. Additionally, we prove that planar graphs with $Δ= 4$ are injectively list $(Δ+ 7)$-colorable and exact square list $(Δ+ 6)$-colorable.
