Gallai-Ramsey Number for the Union of Stars

被引：4

作者：

Mao, Ya Ping ^{[1
]}

Wang, Zhao ^{[2
]}

Magnant, Colton ^{[3
]}

Schiermeyer, Ingo ^{[4
]}

机构：

[1] Qinghai Normal Univ, Sch Math & Stat, Xining 810008, Peoples R China

[2] China Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R China

[3] Clayton State Univ, Dept Math, Morrow, GA 30260 USA

[4] Tech Univ Bergakad Freiberg, Inst Diskrete Math & Algebra, D-09596 Freiberg, Germany

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2022年 / 38卷 / 08期

基金：

美国国家科学基金会;

关键词：

Ramsey theory; Gallai-Ramsey number; union of stars;

D O I：

10.1007/s10114-022-0467-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 K-n contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we obtain exact values of the Gallai-Ramsey numbers for the union of two stars in many cases and bounds in other cases. This work represents the first class of disconnected graphs to be considered as the desired monochromatic subgraph.

引用

页码：1317 / 1332

页数：16

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