A note on the r-hued coloring of planar graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-10-08 DOI:10.1016/j.disc.2025.114829

Xiaoxue Hu , Jiangxu Kong , Weifan Wang , Wanshun Yang

引用次数: 0

Abstract

Let

r \geq 1

be an integer. The r-hued chromatic number

χ_{r} (G)

of a graph G is the smallest integer k for which G admits a proper k-coloring for the vertices such that the number of colors used in the neighborhood of every vertex v is at least

\min {d_{G} (v), r}

. Let G be a planar graph and

r \geq 8

. In this paper we show that

χ_{r} (G) \leq 2 r + 8

, which improves a result by Song and Lai (2018) [12] that

χ_{r} (G) \leq 2 r + 16

查看原文本刊更多论文

关于平面图形的r色着色的注解

设r≥1为整数。图G的r色数χr(G)是最小的整数k，对于该整数k， G允许对顶点进行适当的k着色，使得在每个顶点v的邻域中使用的颜色数量至少为min （dG(v),r）。设G为平面图，且r≥8。在本文中，我们证明了χr(G)≤2r+8，这改进了Song和Lai(2018)[12]的结果，即χr(G)≤2r+16。

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.