周长为 9 且没有较长奇数孔的图形是 3 可取的

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-04-11 DOI:10.1002/jgt.23101

Yan Wang, Rong Wu

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引用次数: 0

摘要

对于一个数，让表示有周长且没有长度大于的奇数洞的图族。吴、徐和徐猜想，在的每一个图都是 3 可容的。Chudnovsky 等人、Wu 等人和 Chen 分别证明了、和中的每个图都是 3 可容的。在本文中，我们证明了每个 in 的图都是 3 有利的。这证实了 Wu、Xu 和 Xu 的猜想。

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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Graphs with girth 9 and without longer odd holes are 3-colourable

For a number $l \geq 2$ , let $G_{l}$ denote the family of graphs which have girth $2 l + 1$ and have no odd hole with length greater than $2 l + 1$ . Wu, Xu and Xu conjectured that every graph in $⋃_{l \geq 2} G_{l}$ is 3-colourable. Chudnovsky et al., Wu et al., and Chen showed that every graph in $G_{2}$ , $G_{3}$ and $⋃_{l \geq 5} G_{l}$ is 3-colourable, respectively. In this paper, we prove that every graph in $G_{4}$ is 3-colourable. This confirms Wu, Xu and Xu's conjecture.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .