A note on Gallai-Ramsey number of even wheels

被引：9

作者：

Song, Zi-Xia ^{[1
]}

Wei, Bing ^{[2
]}

Zhang, Fangfang ^{[1
,3
]}

Zhao, Qinghong ^{[2
]}

机构：

[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[2] Univ Mississippi, Dept Math, University, MS 38677 USA

[3] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 03期

基金：

美国国家科学基金会;

关键词：

Gallai coloring; Gallai-Ramsey number; Rainbow triangle; COMPLETE GRAPHS;

D O I：

10.1016/j.disc.2019.111725

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai k-coloring is a Gallai coloring that uses k colors. Given a graph H and an integer k >= 1, the Gallai-Ramsey number GR(k)(H) of H is the least positive integer N such that every Gallai k-coloring of the complete graph K-N contains a monochromatic copy of H. Let W-n denote a wheel on n + 1 vertices. In this note, we study Gallai-Ramsey number of W-2n and completely determine the exact value of GR(k)(W-4) for all k >= 2. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：5

共 20 条

[1] [Anonymous], [No title captured]
[2] [Anonymous], [No title captured]
[3] [Anonymous], [No title captured]
[4] Bosse C., ARXIV180206503
[5] Bosse C., ARXIV180809963
[6] Gallai-Ramsey numbers of C7 with multiple colors
Bruce, Dylan
Song, Zi-Xia
[J]. DISCRETE MATHEMATICS, 2019, 342 (04) : 1191 - 1194
[7] Cameron K., 1986, Periodica Mathematica Hungarica, V17, P173, DOI 10.1007/BF01848646
[8] 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
[9] EDGE-COLORED COMPLETE GRAPHS WITH PRECISELY COLORED SUBGRAPHS
CHUNG, FRK
GRAHAM, RL
[J]. COMBINATORICA, 1983, 3 (3-4) : 315 - 324
[10] Faudree R.J., 1993, J. Combin. Math. Combin. Comput, V13, P23

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