The chromatic number of {P2∪P3,banner}-free graphs

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-09-12 DOI:10.1016/j.amc.2025.129707

Jiali Long , Kaiyang Lan , Yan Wang

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引用次数: 0

Abstract

Borodin and Kostochka conjectured that for any graph

G

with maximum degree

Δ (G) \geq 9

, the chromatic number satisfies

χ (G) \leq \max {Δ (G) - 1, ω (G)}

, where

ω (G)

denotes the clique number. While this conjecture remains open for general graphs, we prove its validity for the class of

{P_{2} \cup P_{3}, banner}

-free graphs. Here,

P_{2} \cup P_{3}

represents the disjoint union of a two-vertex path and a three-vertex path, and a banner refers to the graph formed by attaching a pendant vertex to a cycle with four vertices. Our result extends the recent work of Lan and Lin [1], establishing the conjecture for a strictly larger class of graphs.

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{P2∪P3，banner}无图的色数

Borodin和Kostochka推测，对于最大度Δ(G)≥9的任意图G，色数满足χ(G)≤max{Δ(G)−1,ω(G)}，其中ω(G)表示团数。虽然这个猜想对于一般图仍然是开放的，但我们证明了它对于{P2∪P3，banner}这类无图的有效性。这里，P2∪P3表示两顶点路径和三顶点路径的不相交并，banner表示将一个垂顶点附加到一个有四个顶点的环上所形成的图。我们的结果扩展了Lan和Lin[1]最近的工作，建立了一个严格更大的图类的猜想。

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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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.