关于周长为 5 的平面图的 2-距离着色的一些结果

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Combinatorial Optimization Pub Date : 2024-05-05 DOI:10.1007/s10878-024-01169-z

Zakir Deniz

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引用次数: 0

摘要

如果相距至多 2 的任意两个顶点获得了不同的颜色，那么图 G 的顶点着色被称为 2-距离着色。假设 G 是一个平面图，周长为 5，最大度数为 \(\Delta \)。我们证明 G 允许 2 距离着色，这改进了 Dong 和 Lin 的结果（J Comb Optim 32(2):645-655, 2016）。此外，我们还证明了当\(\Delta \ge 10\) 时，G允许一个2-distance \(\Delta +6\) 着色。

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Some results on 2-distance coloring of planar graphs with girth five

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Some results on 2-distance coloring of planar graphs with girth five

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 \(\Delta \ge 10\).

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来源期刊

Journal of Combinatorial Optimization 数学-计算机：跨学科应用

CiteScore

2.00

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.