Ramsey and Gallai-Ramsey Number for Wheels

被引：5

作者：

Mao, Yaping ^{[1
,2
]}

Wang, Zhao ^{[3
]}

Magnant, Colton ^{[4
]}

Schiermeyer, Ingo ^{[5
]}

机构：

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

[2] Acad Plateau Sci & Sustainabil, Xining 810008, Qinghai, Peoples R China

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

[4] UPS Amer Inc, Adv Analyt Grp, Atlanta, GA 30328 USA

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

来源：

GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s00373-021-02406-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on 5 vertices.

引用

页数：17

共 50 条

[1] Ramsey and Gallai-Ramsey Number for Wheels
Yaping Mao
Zhao Wang
Colton Magnant
Ingo Schiermeyer
[J]. Graphs and Combinatorics, 2022, 38
[2] A note on Gallai-Ramsey number of even wheels
Song, Zi-Xia
Wei, Bing
Zhang, Fangfang
Zhao, Qinghong
[J]. DISCRETE MATHEMATICS, 2020, 343 (03)
[3] Size Gallai-Ramsey Number
Mao, Yaping
[J]. GRAPHS AND COMBINATORICS, 2023, 39 (06)
[4] Gallai-Ramsey Number for the Union of Stars
Mao, Ya Ping
Wang, Zhao
Magnant, Colton
Schiermeyer, Ingo
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2022, 38 (08) : 1317 - 1332
[5] Gallai-Ramsey number for K4
Liu, Henry
Magnant, Colton
Saito, Akira
Schiermeyer, Ingo
Shi, Yongtang
[J]. JOURNAL OF GRAPH THEORY, 2020, 94 (02) : 192 - 205
[6] Gallai-Ramsey number of even cycles with chords
Zhang, Fangfang
Song, Zi-Xia
Chen, Yaojun
[J]. DISCRETE MATHEMATICS, 2022, 345 (03)
[7] Gallai-Ramsey Multiplicity
Mao, Yaping
[J]. GRAPHS AND COMBINATORICS, 2024, 40 (03)
[8] Gallai-Ramsey number of an 8-cycle
Gregory, Jonathan
Magnant, Colton
Magnant, Zhuojun
[J]. AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2020, 17 (03) : 744 - 748
[9] Gallai-Ramsey number of odd cycles with chords
Zhang, Fangfang
Song, Zi-Xia
Chen, Yaojun
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2023, 107
[10] Gallai-Ramsey number for K5
Magnant, Colton
Schiermeyer, Ingo
[J]. JOURNAL OF GRAPH THEORY, 2022, 101 (03) : 455 - 492

← 1 2 3 4 5 →