The Chromatic Number of (P5, HVN)-free Graphs

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI:10.1007/s10255-024-1029-3

Yian Xu

引用次数: 0

Abstract

Let G be a graph. We use χ(G) and ω(G) to denote the chromatic number and clique number of G respectively. A P₅ is a path on 5 vertices, and an HVN is a K₄ together with one more vertex which is adjacent to exactly two vertices of K₄. Combining with some known result, in this paper we show that if G is (P₅, HVN)-free, then χ(G) ≤ max{min{16, ω(G) + 3}, ω(G) + 1}. This upper bound is almost sharp.

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无 (P5, HVN) 图形的色度数

设 G 是一个图。我们用 χ(G) 和 ω(G) 分别表示 G 的色度数和簇数。一个 P5 是 5 个顶点上的一条路径，而一个 HVN 是一个 K4 加上另外一个顶点，该顶点正好与 K4 的两个顶点相邻。结合一些已知结果，本文证明了如果 G 是（P5, HVN）无顶点的，那么 χ(G) ≤ max{min{16, ω(G) + 3}, ω(G) + 1}。这个上限几乎是尖锐的。

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

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.