Gallai-Ramsey Numbers for a Class of Graphs with Five Vertices

被引：13

作者：

Li, Xihe ^{[1
,2
]}

Wang, Ligong ^{[1
,2
]}

机构：

[1] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China

[2] Northwestern Polytech Univ, Xian Budapest Joint Res Ctr Combinator, Xian 710129, Shaanxi, Peoples R China

来源：

GRAPHS AND COMBINATORICS | 2020年 / 36卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Gallai-Ramsey number; Rainbow triangle; Mixed Ramsey spectrum;

D O I：

10.1007/s00373-020-02194-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given two graphs G and H, the k-colored Gallai-Ramsey number grk(G : H) is defined to be the minimum integer n such that every k-coloring of the complete graph on n vertices contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we consider gr(k)(K-3 : H), where H is a connected graph with five vertices and at most six edges. There are in total thirteen graphs in this graph class, and the Gallai-Ramsey numbers for eight of them have been studied step by step in several papers. We determine all the Gallai-Ramsey numbers for the remaining five graphs, and we also obtain some related results for a class of unicyclic graphs. As applications, we find the mixed Ramsey spectra S(n; H, K-3) for these graphs by using the Gallai-Ramsey numbers.

引用

页码：1603 / 1618

页数：16

共 22 条

[1] A note on the monotonicity of mixed Ramsey numbers [J].