Gallai-Ramsey numbers for rainbow \(S_3^+\) and monochromatic paths
type: Item
instance of: scholarly article
title: Gallai-Ramsey numbers for rainbow \(S_3^+\) and monochromatic paths
zbMATH Open document ID: 1491.05086
author: Xihe Li
author: Ligong Wang
publication date: 2022-03-22T00:00:00Z
review text: For two finite simple graphs \(G\) and \(H\), the \(k\)-colored Gallai-Ramsey number for edge-colorings, denoted \(\operatorname{gr}_k(G : H)\), is defined to be the minimum positive integer \(n\) such that every \(k\)-coloring of the complete graph on \(n\) vertices contains either a rainbow copy of \(G\) (i.e., no two edges have the same color) or a monochromatic copy of \(H\) (i.e., all the edges have the same color). Let \(S_3^+\) be the graph on four vertices consisting of a triangle with a pendant edge. In the paper under review, it is shown that \(\operatorname{gr}_k(S_3^+ : P_5) = k +4\) for \(k \geq 5\), where \(P_n\) is a path of length \(n\), \(\operatorname{gr}_k(S_3^+ : mP_2) = (m-1)k +m+1\) for \(k \geq 1\), where \(mP_n\) denotes the union of \(n\) disjoint copies of \(P_n\), \(\operatorname{gr}_k(S_3^+ : P_3 \cup P_2) = k + 4\) for \(k \geq 5\), and \(\operatorname{gr}_k(S_3^+ : 2P_3) = k + 5\) for \(k \geq 1\).
reviewed by: Lorenz Halbeisen
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 7495512
zbMATH Keywords: Gallai-Ramsey number
zbMATH Keywords: rainbow coloring
zbMATH Keywords: monochromatic paths
MaRDI profile type: Publication
full work available at URL: dmgt.2310
OpenAlex ID: W3011744157
cites work: Gallai-Ramsey numbers of \(C_7\) with multiple colors
cites work: Ramsey Theorems for Multiple Copies of Graphs
cites work: Edge-colored complete graphs with precisely colored subgraphs
cites work: The Ramsey number for stripes
cites work: Q3565877
cites work: Path-path Ramsey type numbers for the complete bipartite graph
cites work: The Erdős-Hajnal conjecture for rainbow triangles
cites work: Gallai-Ramsey numbers for cycles
cites work: Extensions of Gallai-Ramsey results
cites work: Rainbow generalizations of Ramsey theory: A survey
cites work: Transitiv orientierbare Graphen
cites work: Q5548200
cites work: Gallai-Ramsey number of an 8-cycle
cites work: Ramsey-type results for Gallai colorings
cites work: Edge colorings of complete graphs without tricolored triangles
cites work: Improved upper bounds for Gallai-Ramsey numbers of paths and cycles
cites work: Gallai‐Ramsey number for K4
cites work: Q4016829
DOI: 10.7151/DMGT.2310
published in: Discussiones Mathematicae Graph Theory
description: scientific article; zbMATH DE number 7495512