Gallai-Ramsey numbers for 3-uniform rainbow Berge triangles and monochromatic linear paths or cycles

被引：2

作者：

Li, Luyi ^{[1
]}

Li, Xueliang ^{[1
]}

Si, Yuan ^{[1
]}

机构：

[1] Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China

来源：

DISCRETE APPLIED MATHEMATICS | 2024年 / 344卷

基金：

中国国家自然科学基金;

关键词：

t-uniform hypergraphs; Gallai-Ramsey number; k-hyperedge-coloring; Berge triangle;

D O I：

10.1016/j.dam.2023.11.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given two non-empty t-uniform hypergraphs G((t)), H-(t) and a positive integer k, the hypergraph Gallai-Ramsey number gr(k) (G((t)) : H-(t)) is defined as the minimum positive integer N such that for all n >= N, every k-hyperedge-coloring of t-uniform complete hypergraph K-n((t)) contains either a rainbow subhypergraph G((t)) or a monochromatic subhypergraph H-(t). A k-hyperedge-coloring of a hypergraph is exact if all colors are used at least once. In this paper, we get the exact values of hypergraph Gallai-Ramsey numbers for rainbow 3-uniform Berge triangles and monochromatic 3-uniform linear paths or cycles under exact k-hyperedge-coloring.(c) 2023 Elsevier B.V. All rights reserved.

引用

页码：81 / 87

页数：7