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

共 50 条

[31] Arithmetic progressions, quasi progressions, and Gallai-Ramsey colorings
Mao, Yaping
Ozeki, Kenta
Robertson, Aaron
Wang, Zhao
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2023, 193
[32] Improved Upper Bounds for Gallai-Ramsey Numbers of Paths and Cycles
Hall, Martin
Magnant, Colton
Ozeki, Kenta
Tsugaki, Masao
[J]. JOURNAL OF GRAPH THEORY, 2014, 75 (01) : 59 - 74
[33] Gallai-Ramsey Numbers for Monochromatic Triangles or 4-Cycles
Wu, Haibo
Magnant, Colton
[J]. GRAPHS AND COMBINATORICS, 2018, 34 (06) : 1315 - 1324
[34] Gallai-Ramsey Numbers for Monochromatic Triangles or 4-Cycles
Haibo Wu
Colton Magnant
[J]. Graphs and Combinatorics, 2018, 34 : 1315 - 1324
[35] Gallai-Ramsey Numbers of Odd Cycles and Complete Bipartite Graphs
Chen, Ming
Li, Yusheng
Pei, Chaoping
[J]. GRAPHS AND COMBINATORICS, 2018, 34 (06) : 1185 - 1196
[36] Size Gallai–Ramsey Number
Yaping Mao
[J]. Graphs and Combinatorics, 2023, 39
[37] Gallai-Ramsey numbers of C7 with multiple colors
Bruce, Dylan
Song, Zi-Xia
[J]. DISCRETE MATHEMATICS, 2019, 342 (04) : 1191 - 1194
[38] Gallai-Ramsey Numbers Involving a Rainbow 4-Path
Zou, Jinyu
Wang, Zhao
Lai, Hong-Jian
Mao, Yaping
[J]. GRAPHS AND COMBINATORICS, 2023, 39 (03)
[39] GALLAI-RAMSEY NUMBERS FOR RAINBOW S3+ AND MONOCHROMATIC PATHS
Li, Xihe
Wang, Ligong
[J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2022, 42 (02) : 349 - 362
[40] GALLAI-RAMSEY NUMBERS FOR RAINBOW TREES AND MONOCHROMATIC COMPLETE BIPARTITE GRAPHS
Li, Luyi
Li, Xueliang
Mao, Yaping
Si, Yuan
[J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2024,

← 1 2 3 4 5 →