DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2023): 0.5

5-year Journal Impact Factor (2023): 0.6

CiteScore (2023): 2.2

SNIP (2023): 0.681

Discussiones Mathematicae Graph Theory

Article in press

Authors:

Y. Gao

Yujia Gao

Qinghai Normal University

email: gaoyujia@ymail.com

M. Ji

Meng Ji

Tianjin Normal University

email: mji@tjnu.edu.cn

Y. Mao

Yaping Mao

Department of Mathematics, Qinghai Normal University

Center for Mathematics and Interdisciplinary Sciences of Qinghai Province

email: maoyaping@ymail.com

M. Wei

Meiqin Wei

Shanghai Maritime University

email: mqwei@shmtu.edu.cn

Title:

Ramsey and Gallai-Ramsey numbers for forests

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Source:

Discussiones Mathematicae Graph Theory

Received: 2024-02-06 , Revised: 2024-09-23 , Accepted: 2024-09-30 , Available online: 2024-10-19 , https://doi.org/10.7151/dmgt.2566

Abstract:

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 $n\geq N$, every $k$-edge-coloring of $K_n$ contains either a rainbow copy of $G$ or a monochromatic copy of $H$. Given a graph $H$, the $k$-color Ramsey number $\textrm{R}_{k}(H)$ is the minimum number $n$ such that every $k$-edge-coloring of $K_{n}$ contains a monochromatic $H$. In this paper, we determine several exact values and bounds for Gallai-Ramsey numbers ${gr}_k(G:H)$ and Ramsey numbers $\textrm{R}_3(H)$, where $G$ is a special tree and $H$ is a union of stars.

Keywords:

Ramsey number, Gallai-Ramsey number, edge-coloring

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