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Some results on 2-distance coloring of planar graphs with girth five
Journal of Combinatorial Optimization ( IF 0.9 ) Pub Date : 2024-05-05 , DOI: 10.1007/s10878-024-01169-z Zakir Deniz
中文翻译:
周长为 5 的平面图的 2 距离着色的一些结果
更新日期:2024-05-08
Journal of Combinatorial Optimization ( IF 0.9 ) Pub Date : 2024-05-05 , DOI: 10.1007/s10878-024-01169-z Zakir Deniz
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A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at distance at most 2 from each other receive different colors. Suppose that G is a planar graph with girth 5 and maximum degree \(\Delta \). We prove that G admits a 2-distance \(\Delta +7\) coloring, which improves the result of Dong and Lin (J Comb Optim 32(2):645–655, 2016). Moreover, we prove that G admits a 2-distance \(\Delta +6\) coloring when \(\Delta \ge 10\).
中文翻译:
![](https://scdn.x-mol.com/jcss/images/paperTranslation.png)
周长为 5 的平面图的 2 距离着色的一些结果
如果图G的任意两个距离最多为 2 的顶点接收到不同的颜色,则图 G的顶点着色称为 2 距离着色。假设G是周长为 5 且最大度为\(\Delta \)的平面图。我们证明G允许 2 距离\(\Delta +7\)着色,这改进了 Dong 和 Lin 的结果 (J Comb Optim 32(2):645–655, 2016)。此外,我们证明当\(\Delta \ge 10\)时, G允许 2 距离\(\Delta +6\)着色。