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

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

引用次数: 0

Abstract

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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无 K4 小数图和平面图中的边 DP 着色

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.

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

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

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