论文标题
围绕六的平面图的2距离颜色的改进结合
An improved bound for 2-distance coloring of planar graphs with girth six
论文作者
论文摘要
图形$ g $的顶点着色据说是2距离的着色，如果距离的两个顶点彼此之间最多2美元的$ 2 $获得不同的颜色，而$ g $的最少颜色却承认$ 2 $ distance cance and-distance conterance and-distance着色$ 2 $ 2 $ distance chansance chalomatance chalomatance chalomatance chalomatance chalomatance chalomatance chalomatance chomomatance chalomatis chalomation $ q_2（g）$χ$ g $ $ g $。当$ g $是带有腰围至少$ 6 $和最高度$δ\ geq 6 $的平面图时，我们证明$χ_2（g）\leqΔ+4 $。这改善了最著名的绑定，用于围绕六的平面图的2距离着色。
A vertex coloring of a graph $G$ is said to be a 2-distance coloring if any two vertices at distance at most $2$ from each other receive different colors, and the least number of colors for which $G$ admits a $2$-distance coloring is known as the $2$-distance chromatic number $χ_2(G)$ of $G$. When $G$ is a planar graph with girth at least $6$ and maximum degree $Δ\geq 6$, we prove that $χ_2(G)\leq Δ+4$. This improves the best-known bound for 2-distance coloring of planar graphs with girth six.
