拉姆齐和加拉伊-拉姆齐《循环与书籍

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI:10.1007/s10255-025-0009-6

Mei-qin Wei, Ya-ping Mao, Ingo Schiermeyer, Zhao Wang

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引用次数: 0

摘要

给定两个非空图G, H和一个正整数k, Gallai-Ramsey数量grk (G: H)被定义为最小整数N, N≥N,每个Kn的确切k-edge-coloring包含G的彩虹副本或单色的副本H表示grk”(G: H)的最小整数N, N≥N,每edge-coloring Kn最多使用k颜色包含G的彩虹副本或单色的副本H。在本文中,我们得到了一些确切的值或范围grk (P5:H)和grk ' (P5: H)，其中H是一个循环或书图。此外，我们的结果支持Li， Besse, Magnant， Wang和Watts在2020年的猜想。

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Ramsey and Gallai-Ramsey Numbers of Cycles and Books

Given two non-empty graphs G, H and a positive integer k, the Gallai-Ramsey number gr_k(G: H) is defined as the minimum integer N such that for all n ≥ N, every exact k-edge-coloring of K_n contains either a rainbow copy of G or a monochromatic copy of H. Denote gr_k′(G: H) as the minimum integer N such that for all n ≥ N, every edge-coloring of K_n using at most k colors contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we get some exact values or bounds for gr_k(P₅: H) and gr_k′(P₅: H), where H is a cycle or a book graph. In addition, our results support a conjecture of Li, Besse, Magnant, Wang and Watts in 2020.

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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.