Ramsey and Gallai-Ramsey Numbers for Two Classes of Unicyclic Graphs

被引:0
|
作者
Zhao Wang
Yaping Mao
Colton Magnant
Jinyu Zou
机构
[1] China Jiliang University,College of Science
[2] Qinghai Normal University,School of Mathematics and Statistis
[3] Academy of Plateau Science and Sustainability,Advanced Analytics Group
[4] United Parcel Service,Department of Basic Course
[5] Qinghai University,undefined
来源
Graphs and Combinatorics | 2021年 / 37卷
关键词
Ramsey number; Gallai-Ramsey number; Unicyclic graph;
D O I
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中图分类号
学科分类号
摘要
Given a graph G and a positive integer k, define the Gallai-Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_n$$\end{document} contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we consider two classes of unicyclic graphs, the star with an extra edge and the path with a triangle at one end. We provide the 2-color Ramsey numbers for these two classes of graphs and use these to obtain general upper and lower bounds on the Gallai-Ramsey numbers.
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页码:337 / 354
页数:17
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