无 K4 小数图和平面图中的边 DP 着色

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-03 DOI:10.3390/axioms13060375

Jingxiang He, Ming Han

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引用次数: 0

摘要

G 的边 DP 色度数（用 χDP′(G)表示）是 G 的边 DP-k 色度的最小 k 值。1999 年，Juvan、Mohar 和 Thomas 证明了Δ≥3 的 K4-无主图 G 的边表色度数为 Δ。本文证明，如果 G 是 K4 无边图，那么对于某个 Δ=3 的 K4 无边图 G，χDP′(G)∈{Δ,Δ+1}和 χDP′(G)=Δ+1 等式成立。此外，如果 G 是一个平面图，且Δ≥9，并且没有相交的三角形，那么 χDP′(G)=Δ.

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Edge DP-Coloring in K4-Minor Free Graphs and Planar Graphs

The edge DP-chromatic number of G, denoted by χDP′(G), is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of K4-minor free graph G with Δ≥3 is Δ. In this paper, we prove that if G is a K4-minor free graph, then χDP′(G)∈{Δ,Δ+1}, and equality χDP′(G)=Δ+1 holds for some K4-minor free graph G with Δ=3. Moreover, if G is a planar graph with Δ≥9 and with no intersecting triangles, then χDP′(G)=Δ.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.