Improved 2-distance coloring of planar graphs with maximum degree 5

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-08-29 DOI:10.1016/j.disc.2024.114225

引用次数: 0

Abstract

A 2-distance k-coloring of a graph G is a proper k-coloring such that any two vertices at distance two or less get different colors. The 2-distance chromatic number of G is the minimum k such that G has a 2-distance k-coloring, denoted by $χ_{2} (G)$ . In this paper, we show that $χ_{2} (G) \leq 17$ for every planar graph G with maximum degree $Δ (G) \leq 5$ , which improves a former bound $χ_{2} (G) \leq 18$ .

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最大阶数为 5 的平面图的改进型 2-距离着色

图 G 的 2-distance k-coloring（2-距离 k-着色）是一种适当的 k-着色，使得距离为 2 或更小的任意两个顶点获得不同的颜色。G 的双距色度数是使 G 具有双距 k 着色的最小 k 值，用 χ2(G)表示。本文证明，对于最大度 Δ(G)≤5 的每个平面图 G，χ2(G)≤17，这改进了以前的一个约束 χ2(G)≤18。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.