Gallai-Ramsey numbers for multiple triangles
type: Item
instance of: scholarly article
title: Gallai-Ramsey numbers for multiple triangles
zbMATH Open document ID: 1467.05087
author: Fangfang Zhang
author: Xiutao Zhu
author: Yaojun Chen
published in: Discrete Applied Mathematics
publication date: 2021-05-31T00:00:00Z
review text: In this paper, the authors consider finite, undirected graphs without loops or parallel edges. Let \(K_n\) be the complete graph on \(n\) vertices. A Gallai coloring of \(K_n\) is an edge-coloring, such that any triangle of \(K_n\) contains two edges with the same color. A Gallai coloring that uses at most \(k\) colors is called a Gallai \(k\)-coloring. For a positive integer \(k>1\) and graphs \(H_1,\dots,H_k\) let \(GR(H_1,\dots,H_k)\) be the smallest number \(N\) such that for every Gallai \(k\)-coloring of \(K_N\) there is \(i\in \{1,\dots,k\}\) and a monochromatic copy of \(H_i\) in \(K_N\). For a positive integer \(m\) let \(mG\) be a graph obtained from disjoint union of \(m\) copies of \(G\). Within the frames of this paper, the authors study the number \(GR(t_1K_3,\dots,t_kK_3)\) for \(t_1\geq\dots\geq t_k\geq 1\). They obtain upper and lower bounds for \(GR(t_1K_3,\dots,t_kK_3)\) with \(t_1\geq \dots\geq t_k\geq 1\), which they prove to be tight for some \(t_i\) with \(i\in \{1,\dots,k\}\).
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 7352777
zbMATH Keywords: Gallai coloring
zbMATH Keywords: Gallai-Ramsey number
reviewed by: Vahan V. Mkrtchyan
MaRDI profile type: Publication
full work available at URL: j.dam.2021.03.020
OpenAlex ID: W3153951798
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DOI: 10.1016/J.DAM.2021.03.020
description: scientific article; zbMATH DE number 7352777